Valve might have its own controller, but it's well aware that when it comes to Steam and Steam-related activities (playing games, basically), we like to have options. And so, with the most recent beta update of the Steam client, the company has introduced much-improved support for Microsoft peripherals, specifically its console gamepads.
If you hit up the patch notes, released a few days ago, you'll see this helpful paragraph:
Added XBox 360, Xbox One, and Generic X-Input controller configurator support. This allows all recognized controller types to use the advanced mapping features of the Steam Controller Configurator.
It goes on to mention that a lack of "per-controller" identification, the program won't be able to differentiate between "controllers of that type". As such, they'll all share the same settings.
The update also adds support for generic gamepads, however, to work properly, you'll have to assign their buttons "to match a generic gamepad layout". For more details, check out the official patch notes below.