I followed some online instructions for installing StarCraft II from Installing StarCraft II on Ubuntu 14.04 and then it was trying to download eurofixi.exe from an FTP site and not getting any response and having to repeat itself over and over with no success.
The game seems to have downloaded, but there's no executable file to run with Wine.
When I try to redownload the game to play it on Ubuntu 14.04, it gives me the option press play, and when I do this it loads the game in part, asks me to login to Battle.net (not giving me the option to play offline) and then goes pear-shaped.
In the last paragraph in the Installing StarCraft II on Ubuntu 14.04 tutorial it said.
If you encounter any other issues, check out the blog posts I mentioned previously for some tips. If those don't help you and Google fails you, head over to Ask Ubuntu and try to find help there.