Airplay works fine for me on the New AppleTV. I too thought at first that it wasn't working. It seemed, for like a minute or so, to be switch between trying to load the stream and throwing an error saying something like "Unable to Load Content", but after a while, it settled down and the Airplay was stable.
Just a note, I am using a Slingbox 350 and sending Airplay to the New AppleTV using iPad Mini 2 WiFi Only version (Retina Display/No Touch ID sensor).
Slingbox, Slingplayer iOS app, New AppleTV and iPad Mini are all up to date with the latest versions of software and firmware.
I also agree that there should be a native app for the New AppleTV.