There a few Correspondence Chess sites out there that do something like this with chess, but they all require you to register an account or stuff like that. Often they store your game on their database, which is ridiculous because a codestring works just as well.
I tried programming Chess but it was too much work, so here's Chekers. Might make Chess at some point.
Kindly report bugs and give suggestions for other games that could be made into correspondence versions in the reviews!