I've enjoyed this person's videos. His bike is really cool. Can anyone explain how those shifters work and why they may provide an advantage to bar end shifters.

it was going to be... Pedaling around the WORLD

These? Looks like a type of stem shifter.

Should be pretty easy and cheap to try stem shifters. Try them if you like. I never liked them, something about the center of gravity shift, and/or my arm crunched up to get to them.
Can you put them on a threadless fork? Probably not.

Possible advantage is that shifters less likely to get bumped. Another is that shifters are easier to uninstall if needed for boxing bike. Here is picture of shifter bracket.

yea the bar end shifters just got relocated..

I used to have my Rohloff shifter just to the right side of my steerer tube. That meant that I had to take my right hand off of the handlebar to shift.

After three trips, I decided that was not for me anymore. There were too many times that I wanted to be able to shift while having both hands on the handlebar for steering control when going slow on gravel or cobbles or otherwise difficult terrain. And since I needed to make that switch for steering control, that means that putting the shifter near the stem was not the answer, I needed the shifter out far from the stem for leverage. For those of you that are unaware, the Rohloff shifter is a twist grip shifter that can be mounted on a mountain bike type handlebar. I switched to the HubBub adapter which allows me to install the shifter on the end of the drop bar handlebar, and that is perfect for me. This way I can have both hands on the handlebars far out to the sides for good steering control while I can shift at the same time.

First photo before I moved it, the second photo is after I moved it to the bar end position on the HubBub adapter.

Bottom line - if he likes shifters that are in the same location as the old quill stem mounted shifters on that bike that you cited, that is great for him and I am glad he likes it. And, if you never need to shift while going slow on difficult terrain, that may work out just fine. But for me that would not work at all. There were too many times that I wanted to downshift while going up a steep hill on difficult terrain where I needed to maintain steering control.

Back in the 70's, stem shifters were considered a risky newbie setup. Probably not that dangerous but it's still a reach from both brake hoods & bar drops.