Well... first we need to examine what "DOOM" truly is about, right? This way, we can think of a good foundation.
DOOM means two things: VIOLENCE and INSANITY. In any doom-esque fiction HELL would be the go-to environment. Unhinged brutality, unrestrained annihilation, absolute power fantasy, and unnatural rage would be the defining factors of the MC.
I don't really see 'slice of life' being a good addition to any 'horde action' fiction, as action would be constant, relentless, and almost permanent. Maybe a few moments of relaxation that would only serve for preparation for the next wave of 'demons'.
Drama is not really a part of DOOM, so it could feel out of place for a reader expecting a 'true DOOM experience' if that's how you market your story. Some revelations can take place, and that would raise the stakes, but regular 'drama' is not that, at least not in the conventional meaning. TENSION would be the right word.
Exessive violence changes people for the worst, which is why doomguy works: he's not a character, he's a vessel for the player.
Taking that into account, we can construct a doom-esque scenario that works as both storytelling and power fantasy.