It appears that the latest Apple TV firmware update that brought Peer-to-Peer AirPlay to the Apple TV came with some caveats. Primarily that the Peer-to-Peer feature is limited to only the latest generation Apple TV hardware and won't work with older models.
According to an updated Apple support document that was updated after the firmware went live, Peer-to-Peer AirPlay requires a 2013 model Apple TV.
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.
The feature basically allows Macs and iOS devices on different networks to still cast and share content to an Apple TV, making it simpler than requiring all devices to be connected to same WiFi network.