"Win32 compatible" means it uses 32-bit code as opposed to 16-bit code. 16-bit code would be code written for DOS, Windows 3.1, or very early Windows 95.
64-bit Windows can handle 32-bit code, but not 16-bit code.
As far as I know, any game published in 1999 would have 32-bit code, and people have played GK3 on Win7x64, so the problem is not that GK3 doesn't use 32-bit code.
According to computerhope.com, here are some possible causes of the error listed at http://www.computerhope.com/issues/ch000726.htm
This issue can be caused by any of the below possibilities.
1. File is corrupt, bad, or missing.
2. File is not designed for your version of Windows.
3. File is a virus, worm, or other malware file.
4. Hardware incompatibility.
Since you managed to install the game, the most likely problems are with a bad install (maybe an antivirus blocked part of the install?).
Are you using a GOG version of the game or the disc version?
One thing you could try (if you're using a disc version) is uninstalling the game, changing compatibility on the game setup file on the CD to compatibility mode for Windows 98 or 2000, and reinstalling it.