Contrary to expectation, the poles of the magnets are oriented along one of the minor axes of the ellipsoid, not the major axis.
Neodymium magnets in 'ordinary' shapes produce boring 'plinks' when they snap together. Something about the shape of these magnets makes the sound much longer-lasting and entertaining. It is not simply the bounding rebound of two objects made of stiff-but-elastic material. Transfers of linear to angular momentum are clearly involved.
If course, I'd love to know whether these things were 'invented' or 'discovered', and by whom, trying to do what.