http://kindlegamesonline.com
has a rudimentary Javascript chess board that appears to work on a K3, so I suppose it will work in some form on a Kindle Touch. As a non-player with no knowledge of chess rules, I have no idea how good it is.
Being outside the US, one doesn't even have the ability to buy games from Amazon. Hopefully, that will eventually change. So one is stuck with the three games on the site above, newspaper Sudoku webpages (many quite good) and the 2 games on the machine itself. Any others out there guys?