Earlier quoted context omitted.
The official Apple HDMI adapter does the same thing with an SoC in there. The difference is native iOS support instead of a 3rd party app needed to support it.
I still find it hilarious that that’s how the old cable worked, the iPhone encoded an H.264 video stream and sent it to the dongle, which decoded it and sent it down HDMI. Now that iPhones have USB-C they no longer need a custom adapter. A standard USB-C to HDMI cable is supposed to work. I believe.
I am finding it hard to hunt down low level information on how these "adaptors" work. Does anyone know what type descriptors they use? and what a iphone does if you plug one in(I am assuming the lightning to usb physical connector is trivial)
https://www.usb.org/defined-class-codes#anchor_BaseClass13h
update: I found these reverse engineering documents on synaptics displaylink chips. They appear to be a popular manufacturer of such dongles. And it looks like compression is needed there as well.