Well I'm not claiming that these are good games, but I found them mildly amusing and they are defintetly Horror Themed FPS games:
Chasm: The Rift http://www.mobygames.com/game/dos/chasm-the-rift
This game was released around the time of Quake, so it was one of the first 3d FPS games on the market. It had 3d enemies but 2d backgrounds, so it was kind of awkward. It was also one of the first FPS games to feature hit detection where you could blast off limbs and heads. Despite this, it was full of bugs and pretty generic.
Requiem Avenging Angel http://www.mobygames.com/game/window...avenging-angel
I really really liked this game. You play an angel sent to battle human populations that have been possesed by evil angels on the rampage and you also battle these evil angels. You possess both angelic powers and normal FPS weapons. And let me tell you, the angelic powers are brilliant. They range from healing yourself to turning enemies into pillars of salt to resurrecting fallen enemies to fight alongside you. This, IMO, is the most fun power in the entire game. I loved mowing down hordes of enemies, and then resurrecting them to have a veritable army of minions to go through the level with. I routinely had battles of 10 of my minions vs 10 other bad guys. It was fun to just duck out of the room and listen to the carnage and then go in and see who won after the noise stops. Awsome game.
The Thing http://www.mobygames.com/game/windows/thing
While not an FPS, its close. Its basically a third person or first person action game based on the movie The Thing. You can't get much more horor than that.