Off the top of my head: http://codingame.com/ - They support a lot of languages, even Rust!

I also remember an old Java application where you would write AIs for dueling bots, but I don't recall the name.

The folks at https://codegolf.stackexchange.com/ also host several games like that, more often than not competitively, however, and not open-ended or "singleplayer" games. Most accept any language that can take stdin and print stdout.