There are many ways to grow potatoes in containers but this system has some advantages. The first is that it is set on soil so the tubers can root as deeply as they want. Second, by using a wooden box with removable sides it is easier to harvest the spuds at the bottom of the pile.
I must admit to being sceptical about the claimed yield of 100lbs (45kg) from 4 sq.ft. (0.36 sq.m.) Using good soil beds we get around the same yield from 60 sq.ft. (5.5sq.m.) so a 15 times increase would suggest a lot of extra inputs in terms of fertiliser and water. Careful management would be the key to getting such good results.
Most posts suggest using a base frame with four uprights attached to the sides. Presumably other complete side sections are slid over the uprights and more soil added? Remember not to use any sort of treated timber for the box in contact with soil.
The photograph shows 9 halves of seed potatoes (whole tubers cut in half) in one square foot. Even with good fertilisation and lots of water that seems like very close spacing. Potatoes are hungry feeders and very thirsty plants and maybe this is over optimistic?
From my experience with potatoes planted in a dustbin (trashcan) I would use 3-5 seed tubers of a variety known to be good for container growing e.g. Charlotte and maybe 2 tubers for my favourite, Sarpo Mira.
I plan on making one for our 2020 trials to see just what yield we can get from such a small space.
Here are detailed instructions of how to make the box.