I see. Did a bit of digging. Still no clear answer.
http://developer.android.com/training/g ... index.html
http://android-developers.blogspot.com/ ... games.html
Android clearly supports gamepads. I'm not finding documentation though as to whether chrome has access confirmed access. Though I did find this.
With that said, I'm going to have to take an educated guess and say it will. I have a feeling it doesn't work on the Fire because of Silk. FireOS is heavily modified from Android, including the built-in browser.