Because it features a SoC and runs a very basic version of iOS, the Lightning Digital AV Adapter is more than simply a dongle. Apple required an adaptor that would compress video from a connected Apple device, deliver it via the Lightning connection, and then decompress it because Lightning lacks the ability to broadcast HDMI.
The adapter can run Doom since it has a SoC. It required some effort to gain access to the item since, like all of its products, Apple keeps it locked down. Doom is operating on the SoC in the dongle, even though the video shows a MacBook and a monitor.