Well I think of it this way:
Tomb Raider is NOT an adventure game. Adventure games don't use any AI, and nothing can happen unless the programmer tells it to happen.
Games like Final Fantasy are 3D, even if they have 2D graphics. IN other words in Final Fantasy if you move left, the camera swivels left, and then if you press your up button you will now walk in what is previously your left. Same goes for Tomb-Raider. Even though Grim Fandango had 3D graphics, it was still an adventure game because because the viewpoint was glued down and could only move Left or Right (except for scrolling rooms).
So ther you have it, my definition.