This controller looks suspiciously similar to the similar offering from OnLive, but is a great accessory for the Amazon Fire HD nonetheless. It feels very much like an Xbox 360 controller yet has a much more functional d-pad. The price of the controller is slightly offset by the $10 in Amazon coins you'll receive with purchase.
Pairing with the Fire TV was quick and easy and there is no configuration necessary with the supported games. I tested this with the Fire TV version of Sonic CD and it worked well for retro gaming with fast response and a comfortable feel.
One thing to note, however, is that the Fire TV also works with other standard Bluetooth controllers. So this isn't a necessary purchase if you already have a bluetooth controller that works with other android devices. I tried pairing it up with my Mac and it took over mouse control, making the computer unusable until I removed the batteries from the controller (it was continually moving the mouse pointer to the lower corner of the screen).
If you have a Fire TV and want to play games this will provide the best experience. But there are other less expensive controllers that will perform adequately enough to make this one an optional purchase.