As others have said, "purely functional data structure" is a jargon term with a precise meaning--that fact that this is true indicates that data structures can, in fact, be functional in this sense. To claim that "the word 'functional' is purely wrong" is, well, purely wrong; the data structure in Git being described
is purely functional.
Beyond that, you seem to have shown misunderstanding of what that means (despite your claims of "I understand but I disagree"), as the other examples you give DAGs, dictionaries, trees, lists, and this comment thread, do not have the interesting properties of purely functional data structures that make them worth discussing in the context of Git. Namely, the immutability of existing entries.
The thesis of the article isn't that purely functional data structures are Good, or that functional programming is Good. Those are quality judgments that are not present in the article. The thesis is: Explaining Git in terms of the purely functional data structure it uses might be helpful to learning Git.