I did run the reg file and am encountering the same issue, the game works fine when running S3.exe. I'm using it with wine though.

I made a separate topic on this - but I am also unable to play using s3ce.exe - getting asked to enter a serial number. Any workaround or fix for this??

Go to the folder where you installed Settlers 3. Locate the file "regs.cmd". Run it as administrator. After it finishes, you can run the game. I advise, that you run "setups3.exe" first, to set the screen resolution.

Yeah this doesn't work as people seem to keep saying.

you can get it off the ubisoft store, it works without any of these silly fix's cheeper as well