Maybe your eyes played the same trick on you as they did on me.
When I first read the sentence, I also thought that "third" is the third word. Upon rechecking I realized that it is the fourth with the third word being "the".
The original paper mentioned in the article [1] deals with metric TSP, so a triangle inequality must be satisfied. This means that you can actually find a space where the points will be the coordinates.
Anyway, the grandparent solves the Euclidean TSP which is still an NP-complete problem. I will be reluctant to say that it is an easier problem in a general sense.
I agree though that there are better and easier approximations for it.