As far as I can tell, there is no setting in the app to send audio to an AppleTV. However!
I was watching a couple of YouTube videos from my iPhone streamed to the AppleTV. I then went to the Phish App to listen to last night's MSG Show. To my surprise it started playing through the AppleTV. I tested this and realized that after choosing the output from the YouTube App to be the Apple TV, that it then became the default output for the Phish App and voilà!
I know this has nothing to do with web development, but this is a trick i deemed important to share.