They "block" it by reimplementing the entire videoplayer UI. This is unfortunate because it's inferior to the system provided videoplayer UI, and not just due to lack of AirPlay support.

Notice how touching the screen causes the UI to appear immediately, instead of the delay you'd normally expect. Also, the seek bar is much more sensitive and difficult to use.

I've been wondering why they went through the trouble of trying to make a nearly identical video player UI, but I suppose blocking AirPlay seems like a good explanation.