The game will run without any problems through Steam
StarCraft II: Wings of Liberty is a game developed by Blizzard, but it's only developed by the Windows platfom, leaving the Linux users to find other ways of playing it.The only way to play a Windows game on a Linux system is through Wine and StarCraft II: Wings of Liberty has just become a gold Platinum member in winehq.org.
The Wine website indexes the Windows games and applications and catalogs them based on how good they fare. StarCraft II: Wings works flawlessly, at least Ubuntu 12.10 (Quantal Quetzal).
The game can be started it with "env LD_LIBRARY_PATH="/usr/lib32/:/usr/lib/" wine Starcraft\ II.exe"
Given the fact that there is a log of distributions out there with an huge number of hardware combinations, it's impossible to say for certain that it will work on every computer.