From that very long post:
It has been a long-standing question - and one of the most important questions in theoretical physics - whether string theory produces vacua that agree with everything we know about the real world. The first question is whether we can obtain the right particle spectrum. Obviously, string theory has the capacity to produce gravity, the Standard Model gauge group, and particles charged under it that include the observed quarks and leptons. But that's not good enough. We must find a model - or models - which lead exactly to the correct spectrum. No exotics i.e. unobserved particles coupled directly to the Standard Model are allowed if we claim that our favorite background of string theory describes reality . . . . At any rate, they have finally found a stringy model that agrees with the required physics of MSSM, which is a big success.
The MSSM (Minimally Supersymmetric Standard Model), is an expansion of the Standard Model of Particle Physics, not supported by any empirical evidence, that proposes that most particles we know about have "partner" particles which we have not yet discovered, which many scientists think could be supported by evidence obtained from extremely high energy particle accellerators now under construction. It has a number of very useful theoretical and mathematical features that suggest that it could be used to unify disparate areas of fundamental physics and can be meshed with string theory.
A respected commentator at the Physics Forums discussing the string theory model in question notes:
Their masses are not precise, but they do have the right number of generations and the right number of particles per generation and SOMETHING like masses of the right order. Their cohomology classes give them integer masses and they say calculation of actual masses is a task for the future. But yes, I think what they have could be described as a broad brush explanation (not that I can detail that explanation, I have only been a little way into just one of their papers).
In order words, they have come up with a Platonic ideal for theory that would give the masses of the particles in the standard model of particle physics, analogous to say, Newton's theory of gravity, but have not yet done the calculations necessary to get real world values when all of the complexities of real life and the way we measure quantities are considered, in much the same way that a body falling in air behaves differently than a body falling in a pure vacuum (actually, it is even worse than this analogy would suggest because it is theoretically impossible to directly measure the "fundamental" numbers they provide, while it is theoretically possible to measure objects falling in a vacuum).
So, in short, don't put all your money on string theory yet, but the field has made an important breakthrough that could eventually lead to a string theory that can actually predict something like reality.