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Yeah it runs on macs! You sure you aren't doing anything wrong? After you pop in the disc, there should be an icon for "Warcraft III Installer".
 
i bought it for pc awhile back and to my surprise, the cd has the mac installer as well! if you pop the cd in, i think a new window will pop up and you can double click on the installer icon. not really sure why yours isn't working.

unless well your copy is bootleg and it's only for pc :)
 
blizzard ships every game they sell with a mac and pc installer, as long as you have a legit cd that is
 
It will work, you just have to wait a VERY long time. Since the original version that came with the old Warcraft III cds are all PowerPC only, it takes a bit of time to install it as you have to run it through Rosetta. But after you install the updates, everything should be fine and running well.
 
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