It does say in that article that Zabriskie follows this diet purely to enhance his performance and is not interested in the moral or ethical issues. So I doubt if he's bothered about wool or lanolin. He probably has an opinion on honey, but I don't know what it is. The fish is for iron.
No, he's not really vegan, but he's not really vegetarian or meat-eating either. He's following a very personal diet for a specific purpose, which the press has labelled vegan because that's what it seems nearest to, despite differing from veganism on at least one fundamental point. I reckon it's pretty good that the article does mention those differences, seeing that veganism is very much a niche-within-a-minority from the point of view of a conventional Western omnivorous diet. I wonder whether Zabriskie will keep it up in the off season, or even after he retires? It seems unlikely given his stated reasons, but you never know.