Quick update: the much awaited Dota 2 game has been officially released for Linux (Steam). This isn't the "Dota 2 Test" but the real thing so you can play with regular Dota 2 users, as you can see in the screenshot below:

Dota 2 is an upcoming multiplayer online battle arena game developed by Valve. The game is currently available for early test access purchase and will be free-to-play when released. More about Dota 2 on Wikipedia.