I don't know for a fact but it basically is just carving circles around the record (or impressioning them in) and offsetting their centers and radii to generate specular vertices. The 3D shape's rotation becomes automatic as the record rotates. It might be something as simple as just positioning the center of each vertice's circular groove where you want it to appear in 2D, which is to say that all of the circles are around the center of the vinyl and then you offset their centers to position their light glints in different places.
So for 4 points that are the corners of a square you would have four circles with matching radii and just offset their centers a bit. If you want a 1" square then you offset each one by 0.5" in the X/Y to represent the four corners. When you light that up you'll have four glints and when you spin the record the four glints will appear to rotate in-place.
EDIT: I'm not sure you need to vary the radii of the circles at all, it would change the apparent depth of the glints but I don't think it's necessary to produce the animated/rotating model effect.