LLMs aren't leaning what "creativity" is from first principles. They're learning it indirectly, by being trained to reply like a person would, literally, in the fully general meaning of that phrase. The better they get at that in general, the better they get at the (strict) subtask of "judging whether a work is creative the same way a human would" - and also "producing creative output like a human would".
Will that be enough to fully nail down what creativity is formally? Maybe, maybe not. On the one hand, LLMs don't "know" any more than we do, because whatever the pattern they learn, it's as implicit in their weights as it is for us. On the other hand, we can observe the models as they learn and infer, and poke at their weights, and do all kinds of other things that we can't do to ourselves, in order to find and understand how the "deeper superstructure behind these problems" gets translated into abstract structures within the model. This stands a chance to teach us a lot about both "these problems" and ourselves.
EDIT:
One could say there's no a priori reason why those ML models should have any structural similarity to how human brains work. But I'd say there is a reason - we're training them on inputs highly correlated with our own thoughts, and continuously optimizing them not just to mimic people, but to be bug for bug compatible with them. In the limit, the result of this pressure has to be equivalent to our own minds, even if not structurally equivalent. Of course the open question is, how far can we continue this process :).