This resembles ascending a rope using prusiks, which is a lot of fun if you haven't tried it. Great to see a variation the helps people with limited mobility to get around unassisted.
The video for the Vertiwalk looks to me more like standing and sitting in order to ascend.
In standing the seat climbs up a bit to follow your bum, when sitting the floor climbs up a bit to raise your legs into a seated position.
Descending is a bit challenging for my brain to understand.
In an alpine scenario you'd descend by rappelling. I doubt folks in a home want to setup a munter hitch or similar though. :)
“The leader must not fall.”
You would typically descend by rappelling, but it is possible to descend using two prussiks:
1. weight prussik B / unweight prussik A
2. slide prussik A down
3. weight prussik A / unwieght prussik B
4. slide prussik B down
5. repeat
I've never seen this done with two prussiks, but a similar sort of thing is done with two ascenders when rope soloing (e.g., to practice a single move over and over without re-rigging each time).
Dutch.