I get the same problem with the war3.exe file as with the FT.exe.
When you start WC3 what does it say under User name in task manager?
Doesn't work with win7. Also I don't think that's the problem cause other apps have my username.
I didn't have problems during install or when I ran the game, I just clicked the "Troubleshoot compatibility" option out of curiosity, and it somehow fucked up my superbar icon.
Here's a screenshot of my task manager, as you can see the username field is empty and I think it is the source of the problem cause all other games I have tested with have my username there.
Okay this is super strange!
I tried installing with compatibility:XP(SP3 & 2) as admin and not - but it's the same problem as before.
I have no idea how or why it worked the first time around, I need to install it on another PC with win7 to test.
EDIT:
Perhaps we need to take this to the blizzard forums cause I just tested WoW and it has the same problem
Diablo 2, Warcraft 3 and World of Warcraft won't pin to the Start menu and stack properly as they're separate processes. The three games run from \"Launchers\" and World of Warcraft runs a separate instance of wow.exe. If you want to see the stacking behavior, you'll want to try posting in the Suggestions forum.