It’s vastly the same thing with the HDMI adapter. Lightning doesn’t have anything to do with HDMI at all. Again, it’s just a high speed serial interface. Airplay uses a bunch of hardware h264 encoding technology that we’ve already got access to, so what happens here is that we use the same hardware to encode an output stream on the fly and fire it down the Lightning cable straight into the ARM SoC the guys at Panic discovered. Airplay itself (the network protocol) is NOT involved in this process. The encoded data is transferred as packetized data across the Lightning bus, where it is decoded by the ARM SoC and pushed out over HDMI.
Perhaps even more interesting is that Apple could improve the quality with future software updates since the firmware is stored in RAM as opposed to ROM. The poster noted that Apple deemed the quality “suitably acceptable” but *will* make improvements with future iOS updates: expand full story