In 1.0.25, when playing back video with Amazon Prime Video, if you hit Home, the video playback switches to a picture-in-picture window. However there doesn’t seem to be any way to switch the video back to fullscreen playback mode from the remote (you have to reach for the touchpad to move the mouse cursor oven the video thumbnail, and tap twice to first minimize and then maximize the video).
Hitting the Home button on the control should alternately switch to the home screen, and then back to the previous application, so that fullscreen playback can resume. Hitting Home twice would then switch away from a video and then back to the video again.