Ooh, has this game been released yet or is there a dev page I could follow or something? I love to play chess but it's a struggle finding people to play with (plus I'm terrible at it and play just for fun. XD). This is a really pretty set-up too.
A basic Chess AI works like this: 1. Check every possible move. 2. Check for every possible move what the best response for the opponent would be. 3. Simulate the best responses and go back to 1. for every possible response. 4. Take the move that has the best possible worst outcome after X simulated turns. (Or if the AI should be more aggressive, the best possible probable outcome.)
The difficulty against this AI depends on how many turns are evaluated. However processing power is limited and the necessary processing power grows expontially, so a computer can't just simulate 40 turns. (At least not if you don't want to wait a couple of hours before the AI makes it's move.)
The main problem for the AI is how "good" is defined for it. For example a very good human player might sacrifice many pieces in order to get into a subjectivly position he ought to be very good from experience, but this position might be rated as very by the computer.