Controller input must be read from the controller once, then shared with both the Gamepad API and VR UI.

Originally, the controller was read in DrawFrame(). Then, reading was moved to be closer to WebVR frame processing, but this caused DrawFrame to miss (or see duplicate) button events periodically, so controller reading (may) return to DrawFrame().

If we want to read controller state in sync with WebVR frames, we need to queue controller events to the UI, so that it doesn't miss anything.