It appears as though Apple is requiring content providers to expressly allow AirPlay video in order for video to be playable from Safari onto an Apple TV.
To enable AirPlay video in an HTML 5 video player, simply add the following attribute to the video tag:
x-webkit-airplay="allow"
So, your HTML5 video tag might look like (remove spaces from tag open/close):
< video src="/path/to/video.mp4" x-webkit-airplay="allow" preload controls>< /video>

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Nice find!
This is a handy little piece of information that I was going to be needing soon. Thanks for the post, I would have been looking for this in the very near future.
Thanks!