Tor hidden services are all TCP based, and i2pd even can do UDP as far as I know. So, if you can run a game server, and it uses TCP ports, you can run it behind tor.

On the client, however, you may have to use something akin of "local forwarding". You can use socat for that, where you bridge a Tor TCP port and translate it to a port on localhost instead. This should, for all intends and purposes, work (same applies to i2pd - socat is super powerful like that!)