Spacetime relates to four dimensional conceot created by fusion of three dimensions and fourth dimension of time. In Doom (2016) the DOOM Marine has traveled between worlds and through time suggesting not only an inter-dimensional element to the new game's story, but also time travel. It is said that Hell exists outside of space and tme in Doom Eternal.
In addition the new series seems to introduce even more 'worlds' besides the Earth universe, and Hell universe but also a former elemental plane referred to as Argent D'Nur former home of the Elemental Wraiths, and guarded by Night Sentinels. There is also the Maykr (Seraphim race) from Urdak, and there is also the elemental wraiths.
According to Quake Champions (and as some earlier fans theories) the Doom Marine is the same Marine from the original Doom series (Quake Chamions goes on to further imply that the Marine from Doom 3 is also the same figure as well).
With the release of Doom Eternal and ports of Doom 64/The Lost Levels more details have been given. We know from The Lost Levels ending that it sets up the story from the Slayer's Testements. Doom Eternal through flash backs shows that the Doom 64 Marine is the same Marine in Doom 2016/Doom Eternal (when he is found by the Night Sentinels they examine his helmet, exactly like the one seen at end of Doom 64).
The 'time' part of 'worlds and time' (as in time travel) comes in from how Doom 64 relates to 2149 era of Doom 2016. By the time Doom Slayers' sarcophagus had been found in Kadingir Sanctum he had already been fighting Hell's forces for 'thousands of years or longer'. In fact there has been a rather strong conneciton between Site 3 (seen both in Doom 3, and mentioned in Doom (2016) left by the Ancient Martians (actually Night Sentinels) who colonized it from D'Nur. Back when Mars was a lush planet (hundreds of thousands if not millions of years before). Back when the ancient city of Habeth was strong (until it was overtaken by the Forces of Hell), and only the actions of The Hero/Doom Slayer]] stopped it. Site 3 is where the U-series Artifacts were discovered: both Artifact U1 (Soul Cube (2016)/Soul Cube (Doom 3)) and statue of the Praetor suit (Artifact U9) were found (a statue commemorating the Doom Slayer). Other locations there included the Chamber of the Hero which was filled with artifacts related to both the Doom Slayer/Hero (including a certain tablet dipicting the Hero/Slayer fighitng the demons with the Soul Cube), and the Soul Cube itself. Following the Hero's rescue many of Bethian clansmen/Ancient Martians became refugees to earth, seeding the human race.
It was also the Night Sentinels and Makr who made the Marine who changed his physiology imbuing extreme long life (and god like power) to him (turning him into the Slayer) who would fight for millenia longer (at least until he was betrayed).
The "worlds' part of 'worlds and time' refers to the many worlds that Doom Slayer had visited during his 'eternal' battle with Hell. This included D'Nur, Urdak, Hell itself, ancient Mars/present Mars, and various times he defended Earth itself from invasion across time.
In its analysis of this abberation, VEGA observes ephemeral distortions within the fabric of reality: scrambled reflections of the physical world. As the Slayer interacts with this anomaly, a peculiar ripple in the anomaly's composition emerges, seemingly reacting to the Slayer's presence reflexively. The anomoly reshapes itself, calibrating itself to the Slayer, responding to his memory, ancestral, and memetic data, before utimately projecting itself onto the Slayer himself. These change his appearance to many different suits (from those he wore back in his time during Doom 1, to his time in Quake Arena/Champions etc).
This seems to suggest that the single slayer has lived many lives, and possibly across many realities. He has memories of these past lives that can be accessed via anomalies and time travel. This may also explain his use of 'extra lives'. There maybe 'one earth' but actions of the Doom Slayer and Hell may have changed the direction of that history several times creating new 'timelines'. Flynn Taggart may be a version of him one timelie, B.J. Blazkowicz a version from another, Marine from Doom3, yet another of his reincarnated lifetimes.
Spacetime and dimensions
The Halls of the Damned maybe designed around the shape of a weird ancient hieroglyphic, or the schematic to a Demonic time machine. Others think they see a smiling cat on the right side of the installation, or the Virgin Mary.
The phrase "worlds and time" is mentioned in Doom Slayer's bio in Quake Champions. It's also confirmed one of the worlds he has visited is the Arena Eternal.
Chronologically speaking in terms of Quake canon, Quake Champions takes place before Quake Arena games.
The character's bio also includes that he was a survivor of a previous Earth invasion in another world and he carries around the rabbit's foot of Daisy which in part fuels his rage and anger against the demons. This is a reference to him being the original Doom Marine from Doom/Doom II/Final Doom/Doom 64.
The manual changes the description for the Artifacts from '...the other dimension...' to '...the other dimensions...' plural, suggesting that UAC had been exploring multiple dimensions.
There is a reference to an E-BOOK in Doom RPG that seems to suggest research into dimensional and time travel.
- Stabilization Techniques for Rifts in the Space/Time Continuum.
A Codex mentions that Icon of Sin influences spacetime, and warps reality: The Icon's presence warps reality, damaging the implicate order of our dimension merely by existing within it. If the Icon is allowed to remain unchecked it would lead to the total devastation of Earth, followed by a breakdown of spacetime around the planet. The resultant black hole will eventually dragged our entire universe down, casting it into the mouth of Hell as conquest to be absorbed by the Dark Realm.
Art of Doom Eternal
Bound by the forces of chaos, Hell is unlimited by the boundaries of space, time or dimension. Hell itself is a living thing, and entity possessing certain undeniable sentience. An inverse image of the living world, Hell thrives on the destruction of life, and the greater pain and suffering it inflicts into our world, the more powerful it becomes. For all of eternity, Hell has been ruled by an ancient order of evil; six sovereign chapters of the six eldest demonst gods--descendents of the six unholy bloodlines born form the primordial black heart. For an eternity, the Nameless One ahs brought treachery, torment, and war to the outher worlds, driven by an insatiable hunger to secure its dominion over the souls of the living. Many worlds have fallen to Hell, each now bound to ruin, connected by pathways of darkness trancending space and time.
Player Customization and appearances (in Quake Champions and Doom Eternal) are explained with Lore (see above).
Behind the scenes
Until the release of Quake Champions, and especially Doom Eternal much of Doom (2016's) lore, was all enigmatic and mysterious. Leaving fans to speculate what it all meant, and how it related to various games. Some fans believed the reference could be meta in such a way that the DOOM Marine himself might have travelled between parallel Doom universes (different Earths, different series universes). For some only two (the speculation that Doom 2016 was only connected to Doom 64, while believing Doom 3 was entirely ignored beyond occasional "Easter egg"), some argued that doom 3 and 4 were part of the same timeline (see shared universe), but original doom was separate, still for others there existed possibly three separate earths (speculation that Doom 1/2/Final Doom/Doom 64, Doom 3, and Doom (2016) were each a different universe).
The fans further theorized that it follows Doom 64, following Doom 64's ending in which the Marine chose to remain in Hell to insure it would never arise again. In some versions of these theories the original Doom universe is parallel to the Doom 2016 universe, and that he has been pulled into a separate universe. For some, this seemed likely as they took consideration in the way Union Aerospace Corporation functions in both games is very different (one a largely skeptical science community accidentally broke into hell, the other has thrived on occult worship of Hell, and it's part of the company's policies). That being said, Doom 3 never showed us the entire extent of UAC's complexes and settlements (though it made references to several that were not seen directly), and Doom (2016) does make references to sites seen in Doom 3 (but that are not direclty seen in the Doom 2016). Some even made comparisons that certain characters seemed very different as well (General Hayden vs Samuel Hayden if one takes the books into account, which is problematic).
Still other fans did notice connections between the series (Doom 3 and Doom 2016), and that believed the connections were substantial. They argued that the Doom 3 and Doom 2016 timelines overlapped, and Doom (2016) took place four years after Doom 3, giving enough time for UAC to change its policies, and become more corrupt and cult-like (why not? After previous invasions and trips to Hell they realized the place was real, even Dr. Bertruger in Doom 3 made that connection earlier and was using "religious objects' in his research). Then again, perhaps main portions of Mars City (from Doom 3) were blissfully unaware how those working at the top at the Argent Facility were doing (the policies being a tad different there, than in Mars City were there were even civilian workers, generally low-tier UAC personnel, and Earth's military.
Infact the Art of Doom Eternal supports that they originally weren't cultists, and that is relatively a new phenomena among certaon parts of the UAC staff.. It establishes that UAC originaly wasn't cult-like business.. But that UAC splintered into competing factions. It was one faction that arose out of the Lazarus facility... The first cultists arose out of the UAC reponsible for the study and experimentation into Hell, in time drew them to its power (much as was the case with Bertruger), and choosing to open a pathway to evil. They formed a secret society founded in the occult, quickly mutated into cult of ritual sacrifice and blood offerings to ancient demonic gods. Over time they were corrupted by Hell's influence, became united and broke away from the UAC, establighing their own presence on earth. This at least indicates that not all of UAC were cultists like those seen in Lazarus and Argent Facilities in Doom (2016), and that earlier than that they were regular scientists much like those seen in Doom 3.
To be fair, the developers have often been cryptic about details, and never gave full explanations to how each games fit together in interviews, and never specified what is canon and isn't canon. Only referring to rather nebulous idea of "Doom lore' that 'fans will likely enjoy or understand' (even what some might consider 'Easter eggs' Bethesda has treated as 'in-universe' connections between various series).
Perhaps Doom Eternal's perspective sheds more light on the 'truth' of Doom's history. In the game, the inhabitants of Hell, Urdak and Argent D'Nur, speak only of the "Earth Realm" in a singular fashion. As if they are only fighting over one version of Earth (not several parallel earths), and there is only one 'Hell' which has been plaguing this singular Earth with its monstrosities (implying that all previous Doom games had to exist within one shared universe). Still there is no concrete dates for when classic doom takes place in relation to the shared timeline but Doom 3 and Doom 2016 + Doom Eternal lie surprisingly consistent if the timelines are put on top of each other, even including several shared references to certain dates and events that occurred in both game's pasts (and references to same locations on Mars).
The only difference with the series Doom (2016) takes place four years after Doom 3, and it chooses to make very few references to the previous game's story (but some are there if one chooses to look closely enough; archaeological sites at Site 1 and Site 3, the Mixom/Moxim/Mixxom history, Soul Cube (2016) (Artifact U1)'s connection to the Artifact U9... The Ancient Martians of Doom 3, are in fact the Bethian and Sentinel civilization of Mars. The Hero mentioned in the Chamber of the Hero has retroactively been made a reference to the Doom Slayer, etc (implying that not only did Our Hero travel between worlds such as Hell & Argent D'Nur, he also travelled back into time thousands of years, "worlds and time").
There is perhaps enough connections and consistent overlap that to think "that they exist in 'parallel universes'" is actually more speculation than thinking they are part of the same single 'earth' realm talked about in Doom Eternal.
In a series where UAC, continuously attempts to religiously exploit or inadvertently opened passages to hell into multiple 'worlds', if not part of a single timeline (this does seem to be one of the game's way of acknowledging the many iterations of Doom that has come before).