I still don't quite get it. So the center is the barycenter of the planet, but that only gives you the point, not the axes.
The Z axis seems the most clearly defined as it's just aligned to the planet's rotation and the XY plane could be defined as just halving that, but the the rotation of the XY plane doesn't seem to be well defined. The article seems to fix it to the first meridian which is a land reference and subject to drift, so it would be inaccurate. Or there'd be some reference point in the south atlantic where the drift is zero and the rest is relative to it?
Further along this line of discussion, it's always been immensely puzzling to me how sun-relative solar system localization systems handle this sort of thing, since while it's possible to locate the sun and a few stars to track your absolute rotation and one translational axis, where the hell do they get the other two? One reference might be Earth signals I suppose, and possibly Jupiter? But they are all coplanar so the Z axis resolution from triangulation must be complete crap.