The corkscrew pattern on the left side of the kink, looks exactly like the corkscrew pattern on the right side of the kink. It’s possible that the photo doesn’t really illustrate what the article is about.
I know from experience twiddling phone cords as a kid, that it is possible to introduce such a kink into a coil, and then take the kink away as if it never happened. I could never figure out how to explain how to do this, though, I think it involved twisting the cord just so. Sadly, such phone cords are a lot harder to find these days.
If I remember correctly, if you twist an unkinked cord in a bunch of different ways, the way to introduce a kink will soon show itself. Then you can reverse that motion to unkink the cord. Once you get the hang of it, it’s possible to attack a kink that you didn’t yourself create, and unkink it.
Blimey! You’re right, of course! There goes my theory that phone cord kinks have anything to do with this topic. It was such an elegant theory, too, at least in my head!