What layouts does Flexbox solve that Cassowary[0] or GSS[1] layout doesn't?
Pure CSS runs in the browser without a get request (other than the CSS file you are already using, obv.) so it eliminates the need for a grid system like Bootstrap, 960gs etc. The 'grid' is there in the CSS and html where it is meant to be, without the need for @media queries with 10 decimal points and 15 font sizes. It also provides more layout options than currently exist without the need for hacky solutions.
How useful the linked site is right now is questionable though. If you want a IE8+ cross browser & mobile site to rely on flex-box ... it can be done and quite easily, but not with the skeleton examples on that page (but they do point that out themselves).
Basically, constraint solving is harder to understanding, doesn't support wrapping, and is slow.
Because from what I've seen/heard, the Cassowary constraint solver is used extensively in Mac OS X/iOS for UI layout, which AFAIK isn't really referred to as slow.
Plus the constraint solver does operate on a matrix of constraint, which should make it easier to work on GPU.
It is not natively implemented however. Also, to take it further, Cassowary.js could solve for and output to flexbox as a backend.
With https://wiki.css-houdini.org/ there is a chance you could implement custom layout in CSS.