My attempts to train similar networks to learn the rules of chess (just the rules, I'm not even talking about trying to win) have not led to good or steadily improving performance, despite the fact that there's effectively no limit to the amount of training data that can be generated for chess.
There are a number of possible reasons for this of which I think 2 likely ones are that:
1) The networks I'm using have insufficient computational/storage capacity to learn the rules of chess.
or
2) Even if (1) is not the case gradient descent is unlikely to find a sufficiently good near optimum because the response surface is too complex.
As a conjecture, do you think splitting the logic up into several smaller neural networks with different objectives (i.e. for chess, one evaluates defensive maneuvers, one for attack, and so on) would alleviate the problem? Or at least improve the performance of the machine as a whole...
"Trying to teach a neural network to play chess is probably much harder than teaching it to recognize images (at least my very limited experiments suggest this to be true)."
That, sir, depends on your definition of "hard". The rules of chess are, after rules, so you could just set a neural network free within those constraints to play until it found a way to win, and continue to play until it reached a certain performance level.