I'm trying to understand why [John Nash's 1950 2-page paper](http://www.pnas.org/content/36/1/48.full) that was published in PNAS was such a big deal. Unless I'm mistaken, the 1928 paper by John von Neumann demonstrated that all n-player non-cooperative and zero-sum games possess an equilibrium solution in terms of pure or mixed strategies. 

From what I understand, Nash used fixed point iteration to prove that non-zero-sum games would also have the analogous result. Why was this such a big deal in light of the earlier work by von Neumann? 

There are two references I provide that are good: One is [this discussion on simple proofs of Nash's theorem](https://mathoverflow.net/questions/121542/simple-proof-of-the-existence-of-nash-equilibria-for-2-person-games) and [this one](http://www.pnas.org/site/classics/classics5.xhtml) is a very well done (readable and accurate) survey of the history in PNAS.