The reason for this is that iOS allows an app to opt-out of video AirPlay, but not opt-out of AirPlay audio [1]. HBO has opted out of video AirPlay most likely to satisfy its cable provider partners who provide the vast majority of its income[2].
aha. thanks for that explanation. makes total sense to me now. but they really shouldn't include the button if they haven't fully implemented the feature
This restriction likely comes from the studios which provide the content (these deals usually contain DRM restrictions on how the content can be distributed), not the cable operators.
they don't want you watching television except through their boxes
This is entirely untrue. Most cable companies have apps which allow you to stream content via iPad or even Xbox apps.
The whole HBO Go thing is part of a cable wide initiative called TV Everywhere which is entirely about letting you watch your TV content on alternative devices as long as you have a cable subscription. Streaming content is actually a win for the cable operators because it offloads a lot of work from their cable infrastructure. They're actually fine with you streaming content via their network's services as long as you're paying your cable bill.
Excuse my lack of clarity; when I said television I mean the television screen. They are perfectly fine with you watching HBO Go on your iPad but they don't want you watching things on your television except through their cable boxes. Because the cable box contains advertising for other channels you don't currently have and HBO Go does not.
I know, but this info isn't correct. The cable operators are fully allowing the networks to stream to "Over-The-Top" boxes gaming consoles and connected tvs. The two requirements are:
1. Full DRM Solution, this mostly means Widevine or PlayReady DRM. This support is lacking on some notable platforms. The most recent Roku devices don't support full DRM the best they provide is encrypted HLS which can fulfill the DRM requirements for some operators but not all.
2. Authenticated Users, Users must be authenticated with their cable operator. This usually means also having the necessary infrastructure for limiting the number of registered devices etc.
These present is a fairly complex infrastructure component from the operators and HBO Go has been leading the way in meeting these two requirements. This is why you can stream right now to HBO Go on the Xbox and on Samsung SmartTV connected TV platform.
I don't say this as an interested observer, but an active participant I run a services company that actively works with Broadcast Networks on streaming to these platforms. We're literally doing this work right now with large broadcasters.
EDIT: I apologize, I edited this to remove some snark.
1. http://developer.apple.com/library/ios/documentation/AudioVi...
2. http://dcurt.is/hbo-forbes-journalism