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.