When I'm on the game's page in GOG Galaxy and click the green PLAY button the button goes grey while the game syncs with the cloud and then the PLAY button turns green again with nothing else happening.

If I go directly to the game's folder and double click the outcast.exe file I get the message:
"This app can't run on your PC"

The machine is an old Dell XPS720 running 32bit Windows 10.

edit: The answer is that the game requires 64 bit Windows. It says that on the game purchase page but I didn't notice it.

I guess I'll have to download it to a different machine.