A very lucky escape.
The instructor did not appear to do any routine engine failure checks. So far as I can see he did not switch tanks, did not apply carb heat, did not ensure that belts were tight, and did not open the door just before touchdown.
On the other hand he was low altitude and made the decision, in my view correctly, not to bother with checks, but to make a Mayday call and look immediately for a safe landing site.
It's easy to be critical but this chap got three very big things right.
Number 1 - he kept the aircraft flying. Number 2 - he didn't kill or injure anyone on