While streaming to your computer, you are directed to connect the controller into the computer, not the Xbox One. In this form, Xbox 360 controllers will work for playing Xbox One games. You can directly plug in a wired controller, or use an adapter, if you are using the wireless controllers. Good luck.
Is there a wired controller for Xbox one?
The Xbox One’s new controller will be able to function in both wired and wireless modes, Microsoft has confirmed. Connecting the new controller to a micro USB cable will switch off the controller’s wireless functions and allow data to be sent through the cord, a blog post on Xbox.com has revealed.