This all went down in the late 90s. Basically, Wolfram had been employing a lot of people to continue the basic research he did in the early 1980s on cellular automata. Wolfram's claim-to-fame is that he discovered 4 classes of cellular automata (random, stable, periodic, complex). I claim he took these straight off nobel-prize winner Ilya Prigogine who identified these 4 classes for far-from-equilibrium thermodynamic systems - see Nicolis paper (figure 1): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC388547/pdf/pnas.... (Nicolis was Prigogine's student).

Anyway, Wolfram thought he was on to something really big (meaning-of-life type big). But he also founded Mathematica, thought - "hey, i'll just get rich first". And like Jeff Hawkins who put his Palm Pilot money into his first love of brain research, Wolfram funded basic research on cellular automata. And Wolfram wanted the scientific credit for that basic research - hence the NDAs. Now artists (like Andy Warhol and Damien Hirst) have been doing this successfully for years - taking credit for their employees art. Wolfram reckoned he could do the same. But Mr Cook thought otherwise. Fair play to Cook, I say. It's a very interesting exercise, because there's nothing Wolfram can do now. Cook was the one who made the discovery and he told us so. Wolfram wants to undo that, but with the Internet, he can't.

Regarding the actual discovery. It's significance is that it shows us how very simple rules and interactions can produce something complex and regular (a universal Turing machine) upon which intelligent systems can be built. Given that the brain is almost certainly not a universal Turing machine, I believe that Wolfram over-estimated the long-term historical significance of the discovery.