Doom was a truly fun FPS, a happy-go-lucky game design wise, in my opinion, that catered to anyone, and that's not easy to achieve..
That´s a very gory type of happy-go-lucky. I remember playing this game as a kid, and admitedly, to me I had more of a Doom 3 vibe than a Doom 2015. It was legitimately scary. I didn´t play like a run and gun, because I was constatly shitting my pants hearing the groans from monsters somewhere I did´t know exacly where.
But i still like the direction of this one as well. But if I were to make a Doom game that feels old-school Doomey, I´d go much further. I´d really embrace the weirdness and retro-ness and the "I´m an american neardy programer from the 90´s who likes comic books, science fiction and heavy metal who is randomly mashing all this things together into a game" That was the character of the game. It´s been long enough ago for that type of celebration to make sence, and not just feel like being out of fashion, but actually more like understanding the culture and the quirks of a period of time. I´d have hybrid synth/instrumental based heavy metal soundtrack, as a modern nod to the originals midi songs. Synths can enhance te feeling of horror and stress in some ways. I´d have the screen flash when you get the collectibles scatered around the levels. I´d mix the high-tech space-station architecture they´ve got going, with some less plausible parts with this minimalist gothic cathedral type buildings with huge concrete walls and wide spaces, again, as a celebration of the original gameplay-centric level design, that didn´t care much about making the places feel like they had any other function beyond being a game level. I like the excutions, but they could be more refined. They could craft the animations in a way that they gave you the flexibility to still alow player to move and look around while they go on. Sure they look cool, and you wanna have the player see them in all their glory, but jeez, if the player really wants to stop and watch them play out, they will do that by themselves. In a full 8-12 hours game, you won´t want to re-watch them every single time anyways. Haven´t people still not learned that after half-life one?!
Have weird gamey power ups around levels, have a score board at level ends. Modernize where it makes sence, but don´t shy away from stuff that was legitimately cool. We´ve alredy made tons of cinematic and plausible looking games, we have room for weird arcade games again.
But I´m a sucker for kitch, so, that´s just me, I don´t know how marketable you could make such weird game. It would be hard to make something like this, and still make it no look cheap. I think it is doable, but still, hard.