How do I tell if a game on GOG has controller support, or if it is simply a "keyboard game"?

Search for the name of the game on GOG.com (you are already here). On the right (assuming you are on PC) there should be little table with various labels, like "singleplayer mode", "cloud saves" etc. If the game does have controller support, it will be shown there. An example of a game with controller support would be Divinity Original Sin 2.

All games can have controller support:
https://github.com/AntiMicro/antimicro
Really cool utility which maps keyboard or mouse to controller. Just been using it on risen and it works great.