In the context of AI Alignment Theory, a ‘logical’ game is one that we are, for purposes of thought experiment, treating as having only the mathematical structure of the game as usually understood. In real-world chess, you can potentially bribe the opposing player, drug them, shoot them, or rearrange the board when they’re not looking. In logical chess, we consider the entire universe to have shrunken to the size of the chess board plus two Cartesian players, and we imagine that the conventional rules of chess are the absolute and unalterable laws of physics.
Thus, real-world chess is a rich domain, and logical chess is not. In fact, since everything in the real universe is constantly interacting (e.g., ), to consider a conceptual example of something that is definitely, indisputably a narrow domain, we must generally resort to imagining logical (not real-world) Tic-Tac-Toe.