So some of this tech existed before and has just been repackaged with a new name, and some of it is new. The only thing left that I can think of is for 3rd party apps to enable airplay so that the TV becomes the display and the iPhone/iPad becomes the remote. Widescreen angry birds anyone?
The video side of AirPlay is really just streaming MP4 (H.264, AAC) video to the target; it only makes sense for stored video, playing movies that are already in that format.
Key to making it work is that the video is already stored, and can be buffered on the remote end. When you hit pause on the AirPlay source (eg your iPhone), you're not pausing a live stream from the source to the AppleTV; what you're doing is just sending a message *to* the AppleTV telling it to pause. That's why the controls can react without much lag.
Do not expect non-movie 3rd party apps to work over this anytime soon: that would require the app to do its own live H.264 compression of its graphics, which (in addition to draining the battery) requires several layers of buffering that would make most games completely unplayable. Even in the most optimistic scenario, anything you did on the iPhone would take *at least* a second or two before being shown on the remote screen.
Such things could conceivably work in the more distant future through a less compressed, very high bandwidth WiFi link for the graphics, or if the game itself was able to run on the AppleTV and with your iPhone app running *just* as a remote controller, but AirPlay as it stands is not remotely close to either of those ideas.
Also note that Airplay is a standard, of sorts that 3rd party companies are building into their gadgets such as their receivers.
It's not really a standard. It's actually pretty proprietary, but it's built on top of standards, which makes it feasible to reverse engineer. Really, though, the *only* supported receiver for AirPlay video is an AppleTV. 3rd party receivers only accept audio from AirPlay, and to do that, they have to buy and incorporate a specific chip licensed from Apple.
There are third party apps for iOS and OS X that let you turn those devices into receivers for AirPlay video, but these rely on having reverse-engineered the novel aspects of how AirPlay works to advertise, establish, and control the video stream. They also don't work for doing audio-only AirPlay: that part involves an authentication mechanism that hasn't been cracked yet.