This is a really slick presentation!
I have used the related quad-edge data structure to do some very simple mesh things. They’re basically equivalent, but quad-edges “feel” simpler to me. They make no distinction between vertices and faces – you don’t need to do anything weird on the boundary edge; you just treat the inside out “enclosing face” as a regular face, and everything just works. Easier for me to wrap my head, around someone with no background or experience with this stuff.
I also made a little interactive demo demonstrating traversal of the mesh – ctrl-f “little demo” on this page. Not as pretty as the demo in this article, but if you use them side-by-side you can sorta see the resemblance.