The controllers connect to the Shield. You can also connect keyboard and mouse to it.
I find Steam Link to be slow and low framerate though. Sunshine running on the PC and Moonlight running on the Shield seen to do the trick. I also disabled the image sharpening on the Shield because it looks really odd.
Nvidia GameStream being disabled now is a really fucking shitty thing for them to do. Sunshine lacks the ability to change the PC resolution to match the streaming resolution.