http://nedwww.ipac.caltech.edu/level5/ESSAYS/Carr/carr.html
The term ``Population III'' has been used to describe two types of stars: (1) the ones which form out of the pristine gas left over after cosmological nucleosynthesis and generate the first metals; and (2) the ones which have been hypothesized to provide the dark matter in galactic halos. Stars of the first kind definitely exist, but may not warrant a special name. Those of the second kind may not exist, because galactic halos could also be composed of some sort of elementary particle, but they certainly warrant a special name if they do, and they could have many interesting cosmological consequences. Population III stars of either kind could be pregalactic, but they might also have formed during the first phase of galaxy formation.
It is not necessarily required that Population III stars be pregalactic. Some of the arguments for their having a different initial mass function (IMF) would also apply if they formed protogalactically, and this gives rise to a less radical hypothesis, in which the Population III objects form during the first phases of protogalactic collapse. In this case, the Population III stars or their remnants would be confined to galaxies, whereas they would be spread throughout space in the pregalactic case.
Just a point of clarification; if I understood the original article correctly, the star in question is NOT one of the original pre-galactic giants. It appears to be at least one generation removed from that, as it does have SOME "heavy" elements that could not have been synthesized within its own core; hence, there MUST have been a generation of stars prior to its formation that DID support synthesis, and these must be much larger than 0.8 solar masses to get synthesis of anything beyond helium.