One wonders how braking works on a train.

Mostly the same as it would work on a car with a brake shoe applied to the steel wheel.

The only major difference is that they often use a safety air brake system shared across an entire consist (train) that requires “charged” pressure (above atmosphere) to disengage the brake (although I think they have moved to an electronic system that now monitors air pressure in each car individually).

Semi trucks have air brakes that function very similarly. One air source for all brakes, pressure releases, brakes lock on failure.

I think it's actually in an earlier video, and he wasn't able to actually pull the train car due to track irregularity -- but according to calculations he should have been able to if there was a safe way to give it a bit of a nudge.

You're absolutely right; I posted the wrong link.

https://www.youtube.com/watch?v=tfA0ftgWI7U