The Xbox 360 controller, originally designed for Microsoft's Xbox 360 home game console, was the second 3rd-party device to get official Steam Input support (simultaneous with the Xbox One controller and generic XInput devices). Happily using my Steam Controller on a Mac with GeForce Now by having Steam running in the background and setting up the 'Desktop Configuration' to be a generic gamepad.
Simultaneously hold the PS and Share buttons on the controller until the light on top starts flashing.