There’s a lot more going on in this adapter than we expected: indeed, we think the Lightning Digital AV Adapter outputs video by using AirPlay or similar MPEG streaming. Are we off base? Let us know!
An anonymous comment on the post, if correct, goes in to more detail about what’s actually happening, and it’s got nothing to do with Airplay. However, you can buy a $50 adapter that’s more powerful than my first computer. And potentially by a long way.