The IP address shown was an multicast address, which provide a crucial hint as to their setup. Most likely after downlink from Starship the camera feeds are distributed from the test site through their network using UDP multicast, probably without any transcoding and resizing, only remuxed. This allows the feeds to be available to mission control, engineering, employees, etc with minimal delay. Then a separate system, possibly not even at the test site, receives that stream, transcodes/resizes it and feeds it into the mixing and streaming setup. This last part is probably want they use VLC for and what generated the overlay we saw.
The engineer at SpaceX responsible for running the webcasts actually used to be active on r/SpaceX, and has shared some details about how they ran it all.