GOG's version of Bad Mojo did work for me on 64-bit Windows, however that computer had never had QuickTime on it before.
I don't remember for sure what version of QuickTime the GOG version shipped with (was it 6 ?), but if you've installed a different version you might try completely uninstalling QuickTime (might need ccleaner's registry cleaner to completely get rid of it or try Revo Uninstaller), reboot, and try reinstalling the game again.