Google Stadia is due to launch 19th November, However, not all features will be present at launch. As it seems the Wireless Controller will only be wireless when playing on a TV.
This information was noted by a user on Reddit, who noticed some fine print during a new Stadia launch trailer, which points at the Stadia wireless controller only being wireless on TV via Chromecast Ultra.
This was also confirmed by A Google community manager who went on to say:
Both statements are correct. You’ll need a Stadia Controller in order to play games through the Chromecast Ultra that’s connected to your TV.
As for wireless gameplay, this is limited to Chromecast Ultra. When plugged in via USB cable, the Stadia Controller acts as a standard USB HID controller and may work on other platforms depending on the game and setup.
For now, we will have to wait and see when Google will allow users to use the wireless controller with