Very well made, though the AI could be improved
It's great to see a chess game that follows all the rules and has everything put into it. Clearly, you spent a lot of time on it.
There are no glitches or cheating that I can see from the AI--in fact, the AI is mediocre on occasion. Sometimes it makes surprisingly good moves, and other times it makes offensively bad moves. If you could make a difficulty setting, and improve its skill, it would be even better. The things that people think are 'glitches' are probably when the king would move into check if it tried to take a piece, or the person was in a pin that they didn't notice.
I've been playing this game repeatedly since you released it--which is pretty amazing. I didn't know I'd enjoy it to this extent. Adding a multiplayer function would definitely lengthen the game's replayability for other people, and adding more varieties of executions would add to its humor. I think you should make an option to turn off executions if they've been seen before, though, since I found that a lot of the time I wanted to focus on playing the chess and not clicking to get the animation out of the way.
Good job on the graphics, as well as the coding involved. Your instructions were well-written, too. All you need is a tweak to the AI, and maybe options to have different chess sets and piece appearance. Brilliant work here.