I once wrote human-to-human chessboard (for playing chess or checkers with other human being on one device) for Onyx Boox - but it works on Kindle too. You should use it in landscape mode though.
http://ereaders-apps.wieza.org/ - here - there are: chessboard, solitaire and a balls games. The chessboard is only a board when you can move pieces. There is no computer player or anything.