This is an excellent treatment of an esoteric topic, Steve. It smoothly allows people to understand the topic without having to make one's head spin.

You didn't seem to engage much with the idea that universals are essentially linguistic. The first time you show a child a leaf and say "this is a leaf," that name applies to that specific object for the child. If the child shows you a very similar leaf, the child might think it is the same leaf, or a duplicate. You say "that's another leaf." You could show her the first leaf and point out the differences.

You could then show her other leaves and say "these are leaves too" and such lessons could continue, and iterate her knowledge over time.

That process is arguably purely linguistic. The idea of universals might come to her eventually, although more likely someone (a school teacher?) will introduce her to the concept of universals.

I'm not sure if that process involves a language game, or a Kantian impulse to categorize, although I'd argue as an empiricist that not even the idea of family resemblances is necessary to explain the child's learning the meaning of leaf.

One might say what she is learning is language. The theory behind that particular kind of language-learning comes after the fact, a retrospective analysis.