Video game mechanic-wise, he's a glass cannon, but he'd do well in most, if not all, of those universes. The BFG alone is a major advantage.
Lore-wise? Yeah, the only universe I think that could give him trouble would be Warhammer, but knowing Hell in Doom they probably chucked everything Warhammer has at him and the kitchen sink in equivalence over pretty much the lifespan of the entire universe, and he kept on trucking.
The guy is a demigod that's literally too angry to die, immune from diseases, parasites, and mental/conceptual fuckery (sorry, Flood/Progenitors!) because of what that funky Divination Machine did to him (and being what's essentially a fragment of the universe's OG creator given flesh), and he doesn't need to eat, sleep, or rest.
Hell could only contain him and not kill him, and that was basically after they pulled a Hail Mary play.
The undead would be a nothingburger for him -- I mean, he smashed one's skull after being groggy from a nap with his bare hands (Doom 2016's introduction). Resident Evil BOWs? They're not even comparable to demons. And Left 4 Dead's infected/Special Infected? Wouldn't even realize they're there as he vapourized them into nothingness through gun or blade.
A Baron of Hell, especially the types with boiling blood/magma-as-blood shits over Tyrants and other such mutations in capability, and the Slayer regularly chainsawed their heads in two after punching the shit out of them.
Silent Hill? Pft. Hell; 'nuff said. You think Hell wouldn't have tried psychological toriments against him? If anything, the Silent Hill bullshit about "inner-demons" would just make him angrier. He'd literally outdo Silent Hill at its own game!
A Predator? They can be wounded by 20th century weapons and ammunition. The Slayer would literally level the entire jungle to kill it, and given the weaponry he has, it'd take less than a few minutes. Physically? A Yautja, at best, is as strong as a Baron or a Marauder.
The Dragon from Alien 3? Yeah, lots of demons have acidic blood, or their blood is literally boiling or is magma. He'd rip its head off in three minutes and call it a day.
The Combine on Earth? After scaling the Citadel walls (or, ya know, being fired or catapulted to the top because that's how the Slayer rolls) and ripping off Breen's head, he'd probably vanish into the Combine's interdimensional empire and wreck the shit out of it like he did with Hell.
I know it sounds like I'm wanking the Slayer, but this guy is pretty much unwankable because he did this sort of shit canonically with an extradimensional force/realm that'd be on par with the horrors of Doctor Who's Last Great Time War or the darkest parts of the Warp.
The guy would literally make the Chaos Gods either cream their pants (Khorne, Slaanesh), shit their pants (Nurgle, Tzeentch), or delight them (Malal, the Emperor if you buy into the more esoteric theories about him), or all of them combined (Khorne and Slaanesh especially).