Peer-to-peer AirPlay requires a Mac device (2012 or later) running OS X 10.10 or an iOS device (2012 or later) running iOS 8 and an Apple TV third-generation rev A (model A1469) running Apple TV software 7.0.
If you purchased your third-gen Apple TV before then, you’re likely out of luck for the new Peer-to-Peer sharing feature. You can learn how to check which model you have here.