First, that isn’t FI at all. Since he claims to be using Szostak’s definition, none of that fits Szostak’s definition. And any unexpressed other definition he may be actually using wouldn’t make any sense either.
Second, he’s not doing any multispecies comparisons, just pairwise comparisons with human sequences. So “vertebrate specific”, which would presumably require sampling a bunch of different vertebrates for a mass comparison, isn’t a thing.
Third, much of what you say here is word salad. What’s the point of the comparison between humans and “pre-vertebrates” (dubious term)? You bring it up and then immediately drop it. If some differences are due to functional diverence (unlikely to be true for most proteins, incidentally), what does that have to do with vertebrate FI? Just a mass of confused verbiage there.
All gpuccio measures is the similarity of various protein sequences to human protein sequences, one at a time. I will also point out that sharks are not the vertebrates most distant from humans either. What happened to lampreys and hagfish?
You are conducting a cargo cult defense of cargo cult science.