it does not work

That is pretty weird! :/  Are you using the latest snapshot? It does not work in 1.7! You have to move the pieces by left clicking! (Note: Fly exactly above them and punch downwards; There is an invisible slime riding all the chessp pieces!) It should work! I tested it again and for me everything works perfectly fine! :D

I could not figure out how to get the pieces to move. Right click does nothing. Left click deals damage and normal knockback to the pieces. Both bishops and the king for either color didn't spawn. Reset button doesn't work. If you start a new game with pieces still on the board, it just spawns more in on top of the existing ones. 
I don't mean for this to be so negative because I love chess and I appreciate someone making it work in Minecraft, however, I could not get it to do what you were doing in your YouTube video.

You need some method of explanation of what to do with the game and how to use it. A youtube video, writing it in the description, including a written book in the game, just something. While I managed to move a couple pieces around by manually scoreboarding, it needs some form of user interface.
**EDIT** Very cool, lots of good logic going on here. Diamond earned.