I think the author is using the term "purely functional data structure" to mean a data structure that lends itself to an implementation in a purely functional language [1,2].
You can disagree if you want. I just don't want other readers to be misled into thinking that "purely functional data structure" isn't a term of art. Given the number of references to Okasaki's book in this thread, I feel like the interested reader is sufficiently armed to learn more that I don't feel the need to continue this discussion.
You may not find the definition useful, and that's alright. I won't try to convince you.
A round wheel is more useful for a car than a triangular wheel. That doesn't mean it's a "car wheel". It's just as good on a horse wagon or a bike.