Is there a term for when you point a video camera at the monitor displaying what you are viewing and creates the infinite-looking loop effect?
“hall of mirrors” effect?
Video feedback.
Recursion.
I second video feedback.
It’s called “howl-around” here:
http://www.bbc.co.uk/dna/h2g2/A907544
Another vote for recursion, although of course it’s not specific to video cameras; the activity in the OP is merely one example of recursion. It’s not even the only possible form of video recursion: I’ve used the remote-control software Timbuktu to open a screen to a second computer in the middle of my monitor, then turned around and opened a window back to this computer from that computer’s copy of Timbuktu. (I bet the bandwidth czars down in IT were not happy with me).
Video feedback is mentioned here: Video feedback - Wikipedia