I'm not sure of the exact model in the video, but the ones that I've used in the past have pretty detailed instructions on the top by where you put in your detergent. It also says at least 3 TIMES in the instructions that once your money is in and you close the door you have to TURN the door handle to LOCK the washer door to start the machine and you CANNOT unlock it or open it until the wash cycle is done.
It goes on to warn that you need to have everything you want washed inside the machine prior to LOCKING the door.
The ones I've used in the past have been pretty clear that turning that door lock starts the machine and it's locked until it's done.
I just watched the video again and the guy DID turn the handle to lock it. It was after that that the drum started to turn. But I didn't or couldn't see if it was filling with water or not. The water comes in from the back and fills a tank on the bottom that gets pressurized I believe. The way those machines use the water in these is often referred to as Hi Extraction, hence the HE in the model name for these type of washers.
Going by your line of thought, the woman must have already put money in the machine and the guy didn't know it. Maybe she could be seen earlier in the video putting the money in and whoever put the vid up decided to edit that footage out.
When the machine is off/no power to it or there is no money in it, you can close the door and turn the handle and then turn the handle back and open it.