Windows is pretty much the same as Linux, it exposes the raw events from the device and it's up to the app to handle them. Pretty sure the overlay handles that by sitting between the OS and the game and e.g. translating everything to Xbox style controls if the game needs it (And getting out of the way if it doesn't)

Outside of that, well Valve added support for the controller to SDL, so anything using it will be fully supported. But then the game needs to actually be using a new enough version of SDL, otherwise it'll just see a generic controller device, and that can be hit or miss.