Right, so you need to plug it into that, not the TV, since the TV can't send USB data to the Fire Cube that is running the app.
It looks like the Cube doesn't have any regular usb ports, so you'll need to use an OTG adapter like this one to connect the controller to the cube.
EDIT: Looking again it looks like the Cube has separate power and Micro USB ports, so you could use a hub like this to get yourself a couple extra ports
And if you're like me, and would like to charge both headphones and HRM, you can get this:
MakerSpot Micro USB 4 port hub
Just got this yesterday and it connects to the Peloton tablet and charges both my Schosche HRM and Hellas headphones at the same time. It has a short cable, so I used double-sided tape and stuck it to the back of the tablet. It makes it very easy to plug into the hub itself since those ports are very accessible. I plan on simply leaving both cables plugged into the hub and just drape them over the center of the handle bars. Didn't get in the way while I rode, so I'l likely leave them connected all the time and plug in the headphones and HRM at the end of my ride each day.