Wow, ctrl + f this whole thread and only a single mention of one of the best fpp rpgs which just came out not too long ago, Kingdom Come Deliverance, that is the game you want. It's through and through a first person rpg, though it's set in the middle ages so it's swords/archery (no fantasy, no magic).
Highly recommend you give it a play, it's a great rpg, can't wait for their next game.
Vampire: TMB is also one of the better ones along with Deus Ex but you already mentioned that one.