Apparently it will work as a HID device when connected via cable, so it should work as a regular controller, when wired. It is also a bluetooth device, but apparently that's not enabled for use as a bluetooth controller at this time, although it might be in future.
For reference: https://store.google.com/product/stadia_controller
USB-C™ port for charging, wired gameplay and accessories, such as USB-C headsets. HID-compliant
Been using the Nexus Player OG Asus Controller for years, I don't like the Shield Controller but the Stadia one seems pretty neat, any know if there will be compatability with Android TV devices? Even if it's just for gaming/ normal usage?
No. Android TVs are not supported by Stadia at launch.
No idea. We'll see if it can do BT or wired USB on the device once we get it in our hands.
Stadia controller will connect via WiFi to the stadia service directly so I don’t think you be able to use it to connect directly to the Shield. The question will be whether the Shield will work as a chrome cast destination compatible with the Stadia game service.