The Lightning Digital AV Adapter is more than just a dongle, because it has an SoC inside and it runs a super simple version of iOS. Lightning does not have the bandwidth for transmitting HDMI, so Apple needed an adapter that would compress video from a connected Apple device, send it over the Lightning connection, and then decompress it into raw HDMI for viewing on a TV screen or display.

Since the adapter has an SoC in it, it's able to run Doom. Actually getting access to the accessory took work, because Apple has it locked down, like any of its devices. While there is a MacBook and a display shown in the video, Doom is running on the SoC in the dongle.