In many online chess lobbies, I've seen instances of 'engining', where a cheater would open a chess program at the same time as the main game window. He would then set it up so that the opponent's moves are relayed to the computer, then which he would copy the computer's moves, until he (almost always) wins.
As a game developer and moderator, what is there to do about this situation?
Online poker sites use anti-bot measures similar to what you're describing. I recommend the series of articles How I Built a Working Poker Bot for a good overview of how these systems work, and how they are defeated.
I agree with the others who said that there's not much you can do to stop the most dedicated cheaters, but you might be able to prevent casual cheating. (The problem with that, of course, is that then the dedicated cheaters will rule your site.)