This is pretty much what Google TV should have been all along, but Google cares too much about web search and not enough about what people actually want to do on a TV - watch shows and play games. The gaming aspect of this will make it a winner. OUYA's big problem is that it didn't do streaming and was a bit clunky. Amazon has a big game library and just needs controller support. As a parent, a $100 streaming box and…
Most game development companies have a multi-platform approach. Either they accomplish this with cross-platform development tools, or target iOS, Android, and XBox/Consoles separately.
Amazon has already gone through motions to making getting your Android app onto their Kindle Fire devices smoother, so I imagine getting it onto the FireTV wouldn't be much different.
So the story goes, you have a successful game that is gainin traction on multiple platforms and you want to expand your user base. Add game controller support to your android version, and now you're in every Prime customer's living room? edit: This is of course if people purchase the device, so that's the starter.