I found the summary confusing but the article made more sense.
The theory was that there exist configurations of three particles that is stable in a strange sort of way. The strange part is that if a certain configuration was stable then putting the particles in the same configuration but the distances blown up by a certain factor (22.7 if the three particles were the same) gives another stable configuration. So you can keep blowing up the distances in multiples of 22.7 and would get an infinite sequence of stable configurations. These configurations are necessarily quantum and not classical since the distances involved would be much larger than the range of the forces between the particles. (Although even the initial distances are large too, if i understood correctly, you would agree that they _will_ get pretty large at some point).
Now some independent groups have shown the existence of such states with the required blowup. Since similar-particle setup required cooling things down to the limit of present day technology, only _one_ configuration was observed initially. Someone used a system of different particles resulting in a blowup factor less than 22.7 allowing them to observe _three_ of these configurations, essentially validating the theory.
Hope that made sense (IANAP).