Why is it that whenever functional programming comes up, "real programmers" come out of the woodwork to bloviate, only to expose just how little they actually know about the topic?
"Purely functional" in this case is a jargon term that relates to Okasaki's 1996 PhD thesis, available online (https://www.cs.cmu.edu/~rwh/theses/okasaki.pdf). It's a classification for data structures much in the way "regular" or "context-free" or "turing-complete" serve as classifications for grammars.
For a data structure to be "purely functional" (and no, article author does not mean "good" here) simply means that it's implementable in a pure functional language without mutation. Examples of non-functional data structures would be ones where mutation is intrinsic to how its algorithms work: traditional linear probing hash tables, union-find for graphs, etc.
By this technical criterion, the git object graph is clearly a purely functional data structure, sorry.