This is my take on what it would mean for a game to be in the AI genre as opposed to the physics simulation genre. In a physics simulation game, the rules for all the movements of the objects should be based on the laws of physics. Physics is derived from nature itself. We get all our physics equations by mathematical models of the laws of nature. These rules cannot be changed and cannot adapt to the player's decisions or actions. A rock will fall with a constant acceleration and it cannot choose to fall faster in order to hit the player's character.
In an AI based game the objects in the game should be striving to achieve some level of intelligence that allows it to adapt to the environment created by the player's decisions. Most games try to simulate AI by using randomness, but I do not believe this is true AI. An AI based game should try its best to create an environment that causes it's players to believe that it is another human being controlling the game, like a dungeon master.