I too am baffeled by the lack of support for this app. When I heard about the app I immediately picked it up for my iPad 2 and instantly fell in love with all that it offered. Initially it had not occured to me that I could use airplay to stream the content to my apple tv. I recently discovered this viewing possibility through the frustration of not being able to play Apple.com/Trailers on my 27" iMac. I found that I could pull them up on my iPad and a few taps later have it streaming to my 42" plasma instead. Granted it doesn't solve the original problem but it is a great work around. However when I look at the missed functionality advantage with the HBO Go app and airplay I really think HBO or Apple need to address this as I'm not sure if this is problem with Airplay or with the app itself.
As of today I'm running iOS 4.3.2 on my iPad2 and attempting to stream it to my AppleTV running the latest update of 4.2.2 which cited some video playing fixes (http://www.macrumors.com/2011/05/11/apple-issues-new-4-2-2-ios-4-3-update-for-ap ple-tv/) When I start video content as long as my AppleTV isn't 'in use' by another app on my network it shows up as an option from the video player. However after selecting it ONLY the audio is available through the apple tv. When I read the fix notes for the AppleTV 4.2.2 release it cited some fixes that sound like they would fix this. However I've updated my device and still no joy.
I think this in general that the HBO GO app is really going to define the future of the industry in media/content enjoyment. I think consumers (like myself) whom are already subscribing to the content via their cable provider should be able to stream it to their computers, tablets, and mobile devices. The added function of being able to stream it to an AppleTV or output it from an HDMI cable from an iPad2 is a VERY logical function.ROCKDQG 's comments above really give multiple examples of just how flexible of a solution this provides a paid subscriber.
So if its HBO thats blocking the output I think they really have to look long and hard at their decision and reconsider it. If this issue is the result of a bug still within the OS of the AppleTV or iPad or possibly even Airplay then I'm confident Apple will work that out in short order. I only ask that no matter where the 'disconnect' lies HBO or Apple that someone posts something to the public about it and set our expectations.