If your game doesn't give competitors perfect knowledge of the game state, it would make sense for the AI to track previous activity of its current opponent as

If your game doesn't give competitors perfect knowledge of the game state, it would make sense for the AI to track previous activity of its current opponent as part of the 'play state' for making decisions. For instance, if it doesn't know where the enemy is, but the enemy has attacked from this direction every time so far, it would prepare for another attack from that direction. Or if the last time the AI made a given offensive move, the player countered effectively a certain way, it may modify its next offensive to overcome that counter. The longer the game, the more it could appear to be learning to counter its opponent, even though, as you say, it's just making the optimal move given the current state of play.