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It turns out SWAT 3 assumes that the unins000.dat file, created by all our installers, is a MOD file. A non-GOG version will not have this "MOD" and therefore will be deemed "incompatible"...
We will reupload a new version of the installer soon. It will put the uninstaller files elsewhere, so the problem will be gone. In the meantime, there are two ways to get around this:

The easy way: go to your SWAT 3 folder and move any file called "unins000" to a different folder.

The proper way: go to your SWAT 3 folder and rename the unins000.dat file. If you can't see this file, you may have to enable displaying hidden and system files. You can find the appropriate settings by opening any folder and selecting Tools -> Folder Options... -> View tab. On Windows Vista and 7 you may need to press Alt in order to display the folder window's toolbar.

Of course you will have to undo these changes, or install the updated installer on top of your current version, if you want to uninstall the game later.