Would anyone know the whereabouts of the documentation on how to implement AirPlay dual-screen functionality into an app?
This link has very brief, but from what I can see totally sufficient information if you scroll down to "Make the Most of a Second Display".
In short, you register for notifications on a connect to an external display to get a handle to it, and switch between drawing on the two displays by using setScreen(). Besides that, everything drawing related should be "the usual".