You can now play mobile games with a Steam Controller via Bluetooth
The move is a necessary step before the launch of Steam Link app that's supposed to allow users to play their Steam games library on almost any Android or iOS device. The only requirement would be that your phone or tablet (or TV) is on the same 5GHz network as the host PC or it's connected to the computer via Ethernet cable.
The Steam Controller comes with a special wireless dongle that's still recommended to use, but if your smartphone or tablet doesn't have a USB port, you can still pair the Steam Controller via Bluetooth, which, according to Valve, should be “excellent.”
In order to take advantage of the new feature, you'll have to opt into the latest Steam Client Beta and update to the latest firmware. Keep in mind that this still in beta, so there's a chance that you might experience some issues.
source: Valve
Things that are NOT allowed: