If your videocard software is proprietary, and you opted for a pure 64-bit Mint install, this probably means you need the 32-bit display drivers for Wine to use.
This indicates an issue with Wine not being able to use native OpenGL drivers. If it doesn't, don't be too discouraged, try finding out what exactly isn't working and googling any specific errors. Hopefully this works for you without too much trouble.
Run the command above in a terminal, or run your newly-created Launcher, or double-click 'war3.exe' (or Open With 'Wine') within a file browser. Users of other window managers might look for a shortcut like 'Show Desktop' and make note of it, possibly something similar to Ubuntu's Super (windows key) D. i just built my new computer and i am having a problem playing a game, warcraft III, when i click on play warcraft it starts its load up but then stops and i get this msg, 'warcraft III was unable. Hit OK, then give it a keyboard shortcut you'll remember that isn't doing anything else, like Super (windows key) E.