You don't need to be on a LAN network to use airplay.
Set up a hotspot from your iPhone or iPad, or create a wireless network from your mac and have the ATV connect to it.
Airplay is then available without an already established wireless network.
But what you described IS creating an established wireless network. I'm talking about WiFi direct connection. You could go ad-hoc between iPhone and ATV, but that would be a pain unless it's just for one person, which it isn't in my case, and would make any other iPhone that joins the network leech off the host's cellular data.
I have an Apple TV sitting in a room that does not have ethernet connection... because it broke. But it's connected to speakers. Now, there's a Mac there that could host a network that isn't connected to the Internet, but anything that joins that network will lose Internet connection. WiFi Direct is a separate channel totally and lets you go ad-hoc between devices while still maintaining the main connection.