> integrated Steam Controller puck

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.

No, it's part of the Machine. Direct quote from the Steam Machine page:

"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.