You appear to have missed the next paragraph in the phys.org article, Roger: "When we combined that with lunar topography data from the Lunar Reconnaissance Orbiter, we discovered the unexpectedly large amount of mass hundreds of miles underneath the South Pole-Aitken basin."
It was the combination of the lunar gravity model from the Gravity Recovery and Interior Laboratory (GRAIL) mission, the topography data from the Lunar Reconnaissance Observatory (LRO), and some assumptions regarding the subsurface makeup that collectively provided the information needed to derive the existence of a large excess of mass in the Moon’s mantle under the South Pole Aitken basin.
The GRAIL mission provided a model of the Moon's gravity field in the form of a set of spherical harmonics coefficients (to degree and order 1500!!). The GRAIL satellites (two of them) were placed in the same orbit, the only difference being that one led the other. Sensors on the satellites measured the distance between the two. Suppose the satellites are approaching an anomalistically high concentration of mass. This will initially make the lead satellite accelerate away from the trailing satellite as the two approach the mass concentration, but then it will make the lead satellite accelerate toward the trailing satellite after the lead satellite passes over the mass concentration.
In addition to these simple range / range rate measurements between the two satellites, NASA's Deep Space Network (DSN) made very precise measurements of the satellite's orbits when they were over the near side of the Moon. The combination of the measurements from the satellites and the measurements from the DSN were what enabled the generation of the high degree and order model of the Moon's gravitational field.
The topography data comes from the LRO satellite. This satellite carried a laser altimeter as one of its experiments. The altimeter measured the distance between the Moon's surface and the satellite. Once again, NASA's DSN observed the satellite while it was in view. The combination of measurements from the satellite and measurements from the DSN were what enabled the generation of a fairly precise topography model of the Moon's surface.
Combining the gravity and topography models required two key assumptions regarding the subsurface material in the South Pole-Aitken basin. One was that varying thicknesses of crustal material lay over mantle material, with the crustal material being less dense than the mantle material. The other assumption was that the materials were in isostatic equilibrium. This latter assumption may not be valid; it is well established that the large lunar mass concentrations outside the polar regions are in a super-isostatic state. That said, the South Polar-Aitken basin does not exhibit the signs of being in a super-isostatic state.