One of the selling points of Google Stadia is that cool controller, and the way it connects via wifi to Stadia's servers to cut out as much lag as possible - but at launch, it won't be quite as wireless as you might expect. A recent Google video and follow-up post from a company representative both confirmed that the controller will only work via wifi when used with Chromecast Ultra.
Granted, the only way to play Google Stadia games at launch is to get the Founders' or Premiere Edition, both of which come with a controller and a Chromecast Ultra (which you plug into your TV via an HDMI connection and connect to wifi itself). So that's fine. But if you want to take advantage of how portable Stadia makes your gaming experience by taking your Destiny 2 session straight from your TV to your computer's Chrome browser or your Pixel phone, you'll need to plug the Stadia controller into the device with a USB cable.
A bit of fine print in the video below revealed the detail: "At launch, wireless play with the Stadia Controller is only available on TV using a Chromecast Ultra." An employee clarified what that means on Reddit's official Stadia subforum.
"You'll need a Stadia Controller in order to play games through the Chromecast Ultra that's connected to your TV," the representative wrote. "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."
It's an odd limitation, since connecting straight to wifi itself would seemingly allow the controller to skirt many device compatibility issues. Google hasn't provided a timeline for when the Stadia Controller will work wirelessly with more Stadia platforms, but it's a good bet that it will get that squared away before it opens up the service beyond customers who pick up the launch bundles sometime next year.
See how Google says Stadia could have games 'running faster and feeling more responsive' than a console.