So far I've implemented this algorithm in a pretty unoptimized simple way, which results in O(n3) complexity, which is fine for my purposes for now but I want to reach the optimized O(n2) later. So I was reading this material again and now I understand this notation better I think. It's interesting they never explain it in detail here, but basically the way they give this example tells you how you should use the doubly linked lists they mention.

V = list of vertices, circular doubly linked list, data on each node is the actual vertex vector data
R = list of reflex vertices, linear doubly linked list, data on each node is a POINTER to some vertex NODE in V

This is why I was initially struggling with the implementation of the more optimized version of the algorithm. I was trying to store vertex data in a list that was meant to store only pointers to the original data.