(not a lawyer). If you bought the game copies that the AIs are playing, then it seems like you're not making a copy of the game just to have the AI play it.

That kind of assumes that your AI is playing the game through a mechanism like AutoHotKey, generating keyboard or controller inputs that pass through the operating system to the game.

If your AI hooks into or modifies the game code to "play", then it could run afoul of anti-reverse engineering clauses that are common in the click through license agreements. Those clauses may not be enforceable in your jurisdiction. Legal results on anti-reverse engineering clauses are kind of mixed in the United States.

Edit: for reference, there was a software called "Glider" that played World of Warcraft for you, so you don't have to grind to level up. Blizzard absolutely hated the makers of Glider, but it stuck around for a long time, before it was ultimately sued into oblivion.