Not to minimize the usefulness of the explanations and neurological models offered by Kaufman's piece, but I would think that anybody who has paid attention to the language of various discussions of "creativity" would not be surprised by their general direction.
"Creativity" is not a single faculty or gift or event--as Kaufman's phrase "the entire creative process" suggests, it's a word we apply to how we do things, particularly how we devise ways of doing things, generally new or unexpected or particularly clever ways of doing things. Much of the talk about creativity, whether of the artistic or problem-solving varieties, treats it as an almost-mystical ability. This is especially common as a defense among students who claim they lack the special talent to, say, write a competent essay. The complementary foolishness is the student belief that any old spontaneously-tossed-off response is worthy because they're being "creative" instead of, say, lazy or undisciplined or ignorant of conventions and protocols.
But I see that I rant. For non-neuroscience folk, it's worth making lists of words and phrases we use in connection with "creative" activities, then sorting them to see whether the global/high-order-abstractions encompass more concrete terms, and so on. Then match those to your own experience of actually solving problems and making things--how concretely and specifically can you describe exactly what you do and how it feels? Most of the teachers who have guided me in learning non-rote skills have been able to break down their own practices, thus reducing the area of the mystery of creativity a great deal. Because creativity, like luck, seems to favor the well-prepared.