Where is the problem with wifi?
To make it clear - you do not need internet connection or set up wifi network, to make AirPlay work.
But you will need to enable wifi adapter on both aTV and iDevice, as the only other wireless communication channel on these devices - bluetooth - does not have enough bandwidth to transfer video.
http://www.appledystopia.com/how-to/apple-tv-4-peer-peer-airplay-without-wifi/