This is the way I run Warcraft III...
wine "war3.exe" -opengl
I don't know if many people know about this, else I'm sorry...
Warcraft III Frozen Throne TIP (Wine)
Archived thread 417362 from Ubuntu Gamers Arena. Markdown source: Ubuntu_Gamers_Arena/thread_417362_Warcraft_III_Frozen_Throne_TIP_(Wine).md
Yep, that's how I run it too, and it's faster than on my windows box, man I love those folks who make wine. Oh and the computer program is nice too.