Doc, that's called a squeeze chute. They should go into it from the other direction and have their bodies there where those vertical pipes are. Then a lever can be pulled and make a tight fit. That good for shots and such.
He would choke himself because it gets narrower as the part his head is in, goes down. He was being nosey and stuck his head in from the front of the chute. I narrowed up the bottom adjustment so it wouldn't happen again. When we work cattle, I'm usually in charge of putting a butt board right behind their butts in a quick motion, as soon as they enter the vertical area and then squeezing them to be still for the shots... gotta be quick and not on the wrong side of the bar though (short landscape timber) or you can get mashed if they back up too quick and bar isn't all the way in . I've been there too.