I went to the BlizzCon .. great time and I saw their new game Hero Of The Storm - http://www.heroesofthestorm.com/en-us
But I am using Ubuntu 12.04 and when I try to install it, it does not work, nothing happens ... no launcher... no screens ... nothing.
I already have Diablo 3 and WOW installed ... So yes I have Wine installed.
Update: My old answer seems invalid now. There are testimonies on winehq.org that "Heroes of the Storm" is working. I don't own the game and can't verify anything.
Anyone with a step-by-step instruction for Ubuntu: Feel free to post your own answer or improve this one.