It looks similar to a duct access door.
http://www.ruskin.com/category/10~Access-Doors
Before you go and build this, I should point out some things:
1) Digging a hole this deep and getting in and out can be very dangerous, depending on the stability and moisture levels of the soil. Straight vertical walls require bracing/shoring to be sure the sides don't fall into the center of the hole. If a couple of tons of dirt cave-in on a person in the bottom, it is almost impossible to remove them from the hole before they are severely injured or killed.
OSHA Trenching and excavation standards. If you can't make the excavation safely, I would discourage doing it at all. I am surprised this video is allowed to stay up considering the hazard level, and they make no provision to prevent future wall collapse that will crush the bunker.
2) This hole will fill with water if it rains. It will percolate through the dirt around the bunker and seep from the walls. Making it watertight while preventing it from floating out of the hole full of water will be something to work on. Also, when wet, the chance for soil collapse gets much higher.
3) There is no provision for ventilation for the person entering. Suffocation in the box is a real concern. Gas present in the ground can accumulate in the closed bunker.
Please view this video as a cute TV show, rather than a real means to construct a bunker. It is obvious they are trying to get views, rather than show something actually safe, effective, or functional. They make no structural provision for soil collapse, there is inadequate attention given to water intrusion, and there is zero attention given to ventilation. There are tons of other things they are doing that are terribly unsafe (working in a hole without means to get out, sliding into the hole off the side, etc.). They are quite fortunate that they are in a place with somewhat cohesive soil. When it rains heavily, this bunker will be a soaked, muddy, mess.
I would suggest going a different route.