In the second video, it was a case of 'get in, its your only way out' but in the first video, the horse had a choice. The ground work around the trailer helped the horse learn to respect and trust the handler, and convinced the horse it wouldn't suddenly pounce on him and eat him, then from that the horse could decide getting in the trailer perhaps isnt as scary as he first thought.
In the second video the horse was left with no option but to go in the trailer. If he tried to evade the trailer, he got that hinge thing either crank down on his nose, or force his head up. I'm guessing the reason it took the trainer only 8 minutes was because the horse wanted to put a stop to the **** thing on his face, not because he learnt the trailer was a safe, comfortable place to be. It would be interesting to see how that second trainer got along with a normal halter, or if the horse will load in a normal halter after being trained with the cranky one.
If I was going to try either method, it would deffo be the first! I suppose the first is kinda similar to mine, I do back and forward instead of circles until Alli goes 'actually mum, I'd prefer to keep going forwards up the ramp instead of backing up'