While I've never tried it in that way, I understand it should function as a standard USB game controller when wired, but its real gem would be fully leveraging its wireless support.
The problem is that Stadia controllers use wireless in the sense of WIFI, not bluetooth. This means that in order to make them work not only is the RE work even harder, but you'd probably have to create a completely new driver since I'm unaware of any other device that can input commands from the internet; whereas with bluetooth we already have extensive tools to deal with it