Adventure games became FPS as early as 1992 (only one year before DOOM, so maybe I'm not making much of a point here) with the coming of Ultima Underworld.
That’s a fair point. I suppose if I wanted to focus on the first person perspective I could have mentioned Myst coming out the same year as DOOM, though I doubt it was even the first FP adventure game.
It was a real time action-adventure game with puzzles. TR made point and click adventures obsolete as they drove a puzzle-event bound game with free exploration. OTOH, text adventures would still be featureful and playable as they achieved incredible things very expensive to do with graphical games.
If Tomb Raider is an "adventure game" so is Donkey Kong. Tomb Raider is basically a platformer like Donkey Kong but in 3D. Neither made actual adventure games "obsolete" because taxing your hand-eye reflexes is a different sort of fun than taxing your brain.
Also, definitively, what killed the adventure genre would be the PS1 survival horrors. You have everything there: items, combinations, loads of puzzles, action and a shitfed perspective.
Silent Hill, Resident Evil, Parasite Eve...
Pretty much the definition of an old 'point and click' aventure with action points.