This is part of the controller, not the Machine. Unless you mean software integration, then it's on SteamOS and the Steam client, both of which can run on custom hardware.
You can use the steam controller over Bluetooth, the puck is really a 2.4GHz dongle that (allegedly) gives better performance/reliability of something.
The Steam Machine has the 2.4GHz dongle part as well as a Bluetooth adapter.
"Steam Controller's wireless adapter is built right into Steam Machine for direct pairing. "
It has dedicated hardware for pairing with Steam Controllers without needing a puck adapter plugged into a USB port.