The Doom Marine's moments of compassion/Pet the Dog are yet ANOTHER callback to the classic games. Given that the reason for the original Doomguy being reassigned to Phobos was breaking every bone in the body of/quite possibly killing the "Superior" Officer who ordered him to open fire on unarmed civilians; The Doom Marine silently staring at the body of a horrifically mutilated UAC worker during the administrator's speech may be a lead-in for a future expansion/DLC or may be another subtle hint that he MIGHT be the same person.
One wonders how Olivia Pierce eventually was corrupted whereas Samuel Hayden was able to resist, to the point of calling Olivia weak-willed. Then we realize that there is one thing that Olivia still has that Hayden no longer does—a soul. Think about it: flesh-and-blood Hayden died quite some time ago; cyborg Hayden, while a perfect copy of his brain patterns and strong (comparatively) moral center, is not technically a living entity. Therefore, he was unable to be corrupted by the use of Argent energy or by the whispers of demons.
To be fair, Samuel is explicitly more-cyborg and less-human than characters such as Motoko Kusanagi. While a good chunk of his brain IS cybernetic, his brain, with at LEAST his temporal and frontal lobes "intact" (likely meaning with no surgical or cybernetic modifications) WERE transplanted into his new body, with his other functions enhanced by his new body's "Plasmatronic" Processing Core—which is powered by an Argent Energy Storage Device. Though, he could have at least sprung for a more natural voice synthesizer...
Olivia is a cyborg as well as Hayden. But the technology back then was not as advanced as the tech that made Hayden a cyborg, and the process caused, and was still causing her, near-unbearable pain. Because Olivia was such a fanatic, she refused to take anything that would help her deal with the pain, because it would dull her focus and mental clarity. The only way she would have been able to make the pain stop normally would have been either to be confined to a wheelchair for the rest of her life or to do the same thing that Samuel did, neither of which Olivia wanted. But still, this kind of thing takes its toll on you, and this situation was most likely the demons' "in" for getting their claws into her.
Hayden was already in his cyborg body before he'd met Olivia, and long before Olivia's Scoliosis prompted the need for her exoskeleton. Not to mention, it's mentioned in the Data Logs that while Hayden's body is long dead, "his soul will live on forever" thanks to his immortal robot body. The real reason I think Olivia succumbed to demon-worship is that while Hayden has no way (or reason) to feel pain anymore, Olivia's refusal of medication left her in constant agony, and that pain was the in for the demons that corrupted her.
The reveal that heavenly forces are aiding the Doom Marine could be a reference to the Bible story of Samson, another reckless berserker given fantastic physical prowess by God. Oddly enough, for as much as the Doom Marine acts like a Jerkass, he's actually less of a jerk than Samson is.
The voice-over during the intro can also be explain through the reveal, likely delivered by whomever is his "handler" in the heavenly side of things. This is supported some by the command to "Rip and tear, until it is done," as hellish forces would rather he not start at all, while those who do support him would likely rather he not stop, with only heaven as a contender as for who would want such a targeted version of a walking weapon of complete annihilation.
The Demons explicitly DIDN'T back stab Betruger in Doom 3, or Olivia in this timeline/universe, despite outright VOICING their displeasure that she "allowed" the player character to be awakened. if the theory that the Doom Slayer was the Traitor who caused the fall of Argent D'nur in exchange for "resurrecting" a lost loved one, they might be TERRIFIED of creating ANOTHER similar-powered Nemesis.
Why is Hell so sparsely populated in this game compared to previous Doom games? Simple: As this game takes place after a number of historical events that parallel the previous Doom games, the Doom Slayer has already thinned out the demon hordes rather significantly.
Or the rest of them are cowering away from the battlefield.
Or the remaining population has moved to Mars?
The Doom Marine's complete lack of patience when it comes to preserving Argent Energy makes sense when you realise Argent Energy is a actually a product of his homeworld that Hell invaded and absorbed them for. Having to listen to someone try and justify deliberately opening portals to Hell and risking demonic invasion just to exploit the thing that got his home destroyed...it's no wonder he keeps smashing anything associated with it.
Even more pointedly he did actually stop and listen once or twice on the off chance that maybe the humans had a point. After all his people originally owned the Argent energy source and they were doing just fine for a long time. But then the person trying to talk him down gave him bad reason after bad reason to keep using Argent that was effectively based on self interest or the greater good at the cost of personal loss for everyone involved. Given his own experience with losing his son that prompted him to let hell in on the promise of having him returned the Doom Marine is well aware of what would have eventually happened Olivia or not.
The tagline: "Fight Like Hell" has more meaning than just killing everything in sight. The Doom Marine has, through whatever means, gained the ability to harness demonic energies and runes and the strength to shatter his solid metal restraints with barely any effort. He fights like Hell. This also flows into his sheer dis-regard for any of the excuses, reasonings, or pleadings of Hayden, given the likely reason he's resisted temptation of Hell is by never bending, never even considering having any other dealings with Hell aside from ripping and tearing everything demonic in sight. Aside from the death of his pet rabbitpreventing any sort of diplomatic solution to their conflict.
Ironic, given that a traitorous Demon was the one that gave the Marine his powered Praetor Suit in the first place. In a sense, the one seeming demon that the Doom Marine didn't kill (as far as we know) was the one that empowered him with the power of Hell itself to go slaughter the rest.
Considering the Praetor Suit was forged in hell and everything is of Argent AKA hell energy, and the Doom Slayer may be of Hell, the chainsaw and Glory Kills causing enemies to burst into health and ammo drops not only makes sense in mechanics, but might fit the lore as well. The suit literally feeds off the demonic energy of your victims and fashions it into ammunition and repairs damage you sustain. The Doom Marine literally kills to stay alive.
A bit of possible Gameplay and Story Integration: While it is obvious that Doomguy is a badass, he is comparatively fragile, and if you are playing on higher difficulties, he tends to die even easier. Why is it then that the legions of Hell are scared witless of him? Just what makes him so powerful? His armor is described as indestructible, yet we see even imps tear him apart if the player makes a mistake. He moves fast, but so do a lot of demons. He deals a lot of damage, but he uses human-made guns to do so, something everyone has access to. So, what makes Doomguy so special? One word: checkpoints. Introducing gameplay-concepts such as reloading checkpoints and saves into the actual lore would explain a number of things, such as the nature of the blessing he received from Heaven, or why the demons bothered with entombing him on the first place instead of just killing him. After all, no matter how many times they killed him, he just kept coming back, so they had to imprison him in a way he couldn't even commit suicide and return to a previous checkpoint.
The lore of the Night Sentinels is a massive, civilization-wide case of History Repeats. The Night Sentinels were guardians in service to the people of Argent D'Nur, charged with watching over the Wraiths—the original source of Argent Energy. This was a sort of double duty for them, because while the Argent Energy was incredibly valuable, its source was also actively dangerous, requiring vigilant military force to restrain. This worked fine for them, until the nameless betrayer turned on them and opened the way for demons to overrun their entire world. So far, so good, right? Now substitute "UAC" for "Night Sentinels," "humans on earth" for "the people of Argent D'Nur," "Hell" for "the Wraiths," and "Olivia Pierce" for "the nameless betrayer". As the demons themselves put it, "treachery resides in all things and we shall set it free." The one and only difference that will affect the outcome this time is the presence of the Doom Slayer on Mars.
One might question why Elite Guard armor has chips that are compatible with the Praetor Suit. It stands to reason that Elite Guard's armor is actually the UAC's attempt to reverse-engineer said Praetor Suit, hence why they are similar enough to allow this to happen.
The reason the Slayer uses his third and fourth fingers to push buttons is that he doesn't want anything to happen to his trigger finger.
The Doom Slayer's Glory Kills are extremely brutal, but also very quick and efficient, with every Glory Kill managing to kill its victim in less than 3 seconds. This actually makes sense, however, as the Doom Slayer spent so much time in Hell fighting and killing demons that he became intimate with their biologies and the quickest way to kill them. However, adding to this is that the Praetor Suit absorbs Argent Energy, and the Slayer Testaments mention that the Doom Slayer drew strength from those he killed. Glory Kills don't just efficiently kill each demon, they also allow the Slayer to absorb Argent Energy from the body (in the form of health pickups) while killing them.
Why do the demons go after the Doom Slayer in waves, instead of flooding him with bodies (like in the classic cover art)? Maybe it's gameplay / story segregation. Maybe they can only warp so many in at once. Maybe... they know he has the BFG, and that if they send one massive wave at him, he'll just pull it out and turn them all in to so much fine red mist.
While most of the bodies the demons get their hand on becomes red paste in short order, the bodies of the elite guard scattered throughout the levels are almost entirely intact and unbloodied, so much so that delicate computer chips can be salvaged from each body in perfect working order. Then you read in the codex that each guard is installed with a kill-switch in case of a mutiny, which only two people had the power to flip; Samuel Hayden and Olivia Pierce. The demons haven't mutilated them because they were already dead; wiped out by the traitor with the press of a button.
After defeating the guardians and claiming the Crucible, the Doom Marine is saluted by the Spirits of several of his fallen Night Sentinel comrades before being tethered back to Mars. Given Hell's love of organic technology throughout the series, what if the biological components of the guardian golems was fashioned from the remains of Fallen Sentinels, the ORIGINAL wielders of seven energy...
The Reveal of the origin of the Doom Slayer's armor and power coming from a demon betraying his kind to supply the former and a Seraphim blessing him for the latter. Just how bad is Hell that one of their own helped empower the man that wants to wipe every trace of Hell out of existence?
Also, the Doom Marine's Praetor Suit is pretty advanced and able to interface with UAC technology easily to the point of being able to store and potentially integrate VEGA's software, though naturally not on the same level as the Hell-powered supercomputer he was pulled from. So just what or where the Hell did a demon make this armor from?
It could be that the guy who helped Doomguy was the betrayer of his homeland, who sought to atone for his mistake by allying with his former comrade. Who else would know how to make Night Sentinel-worthy gear?
The demon hordes are referred to as "the Slaves of Doom". And it is the nature of slaves to rebel...
Even as the Doom Slayer is said to be here, some demons are still attacking each other. It's not that Hell is horrible; it's that the demons are so kill-happy, they'll lay waste on their own kin for little reason.