Unless I've misundertood what's going on, this star should be characterized as a primordial galactic star, not a primordial pre-galactic star. The first pre-galactic stars are believed to have been enormous beasts that coalesced out of the detritus of the Big Bang (hydrogen, helium and a wee bit if lithium), and as such, would have burned fast and furiously for a brief period of time (in cosmological terms, at least). These would have produced small amounts of heavier nuclei that we see in the primordial galactic stars such as the one in this article, which explains why this star has SOME heavy nuclei, but far less than later generation galactic stars.
How "pristine" is the gas still going to be after all this time, even if it was kind of a ho-hum sun?
The observeable part is the surface, from which the photons are emitted that we see in our telescopes. This should be virtually the same composition as when it formed, as the fusion process and byproducts are confined to a central core region of the star. The energy produced there is transported by radiation and convection processes to the surface, but the byproducts remain within the core. Thus the material at the photosphere's surface should be pretty much the same as the original composition (i.e., 12 billion years ago), unless the star has been accreting matter from another stellar body, but at 0.8 solar masses, that would be rather unlikely.
Except helium doesn't seem to remain within the core. So the hydro-to-helium ratio would still be altered from what it was at the beginning.