Well I would say this about that choke looking at the picture.
Even thought the officers arm is in fact under the mans chin, his other arm is not behind the head pushing the head forward and this causing a windpipe choke against the arm under the chin.
That would be the sleeper hold or rear naked choke. That choke can deny a person air, and if held long enough is basically strangulation.
I do not see that here at all.
Also, it is not a choke that is constricting the arteries on either side of the neck.
Neither the man nor the officer is in a proper position for the officer to have the leverage to do that sort of choke which DOES NOT deprive the victim of oxygen to the lungs, but rather causes the victim to pass out due to lack of blood to the brain.
It looks to me like all that is going on here is that the officer is securing the man’s head, which I must say is large.
There are lots of choke types, you are right that this wasn’t a rear naked choke, it was a lateral vascular. It chokes both the arteries and veins on both sides of the neck. It also can choke off air supply if done improperly.