The new Doom feels really new because it goes against everything FPS we've seen in the past 10+ years, but in reality, i really felt nostalgic while seeing it in action. It felt like Quake III Arena and Unreal Tournament in gameplay/execution. It really is a throwback to the age when shooters were just for fun and didn't really attempt at too much realism.
To me it's a "copypasta" in the way that it glued together what was best from Doom, Quake and Unreal, and then sprinkled in a bit of its own magic. The atmosphere is VERY Doom-like, but the frantic pace at which the action develops reminisces me of Unreal Tournament, while the level-design echoes a lot of Quake II/III for me. At the same time, it has upgradeable gear, a very modern mechanic, as well as enemies dropping weapons/health when killed in specific ways (Glory Kills and exploding enemies cause them to drop health, killing them with the chainsaw causes them to drop ammo).
Its focus is almost exclusively in the gameplay, so much so that it lampshades itself by having the protagonist cut off dialogue by punching monitors, and go explictly against the desires of the "quest-giver". There are very few moments with no player interaction, and they're brief enough, no 10+ minutes cutscenes as we've been seeing with recent games.
All in all, i think it's really innovative because it really manages to give a really TIGHT shooter experience, for people that liked shooters as they were way back in the day. It goes against the more recently established formula and shows that old-school shooters still have a place in this day and age, and that more modern graphics and 3D assets can enhance rather than detract from this experience. That's how it's innovative, not because it created something new, but because it revived something old in a new and improved way, when everyone thought that was never going to happen.