I just completed some quick testing on my 16GB Nvidia Shield TV:
Wireless Xbox 360 controller - works as expected and correctly indicates that it's paired as player 1 rather than endless blinking.
Wired Xbox One Controller - works as expected.
Wireless Xbox One Controller - not working. No action from controller button presses and no light on dongle when attempting to pair.
Wireless Xbox 360 controller - works as expected and correctly indicates that it's paired as player 1 rather than endless blinking.
Wired Xbox One Controller - works as expected.
Wireless Xbox One Controller - not working. No action from controller button presses and no light on dongle when attempting to pair.