If this star masses as much as ours, but has no iron core, it would in fact take up a much larger volume of space. Kinda hard to tell from the crappy article.
If it is that close, and still burning, it must be burning very "cool" indeed. Ours is at around half-life and should be around another 4-5 billion years. If this other star was putting out half the energy ours is, it's "life" would be roughly doubled depending on what it can do with its fuel supply and the by-products.
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.