But they answered the question. Valve can only guarantee that games are compatible with Steam Overlay compatible games. They don’t want to commit to a “yes” or “no” for stuff outside Steam, and then be liable for that answer if it does not work as advertised and then get sued to the ground. So you cannot blame them.

I don’t know on Windows, but on Linux you most likely can use the controller to play on any game. It’s just not supported and guaranteed by Valve.