Power windows in cars often come with automatic reversal mechanisms, which are designed to detect obstructions and prevent the window from closing on them. I don't see mention of such a safety feature here, though.
Maybe making the Chicken Squisher 3000™ close very slowly would reduce the likelihood of a squish event? In the video, it's not like the door slams shut, but it's not slow.
Or maybe chickens, dumb as they are, have quick enough reaction speed that the danger of squishing is negligible.