The ecosystem model in which loss of biodiversity reaches a tipping point upon which the food web collapses is basically as old as practical numerical computation being available for general research -- the 1970s. The question of how precisely you can characterize the tipping point is a key one in network theory/ecology/biology. So as we have good data on certain ecosystems, such as around agriculture and in certain well-studied areas of rainforest, it is of interest to know whether the next species to go locally extinct will collapse the local ecosystem, as does happen (this or similar network phenomena may be a major cause of the colony collapse epidemic in American honeybees currently, which is chicken-or-egg devastating to biodiversity in areas in which it occurs, and is of course of huge financial concern to agriculture).

So the relation of these kinds of papers to Climate Change and the Anthropocene extinction (i.e. humans destroying habitats and causing things to go extinct super quick) has been warned about for decades. That's the pop sci magazine reporting.

This is awesome new research because they applied this technique -- a rather tricky one in general -- to a very tricky fossil record (for which they also expanded the existing model), and got it seems rather conclusive results. So it probably speaks to the strength of the theory in general, but I would always be cautious about that, since being a powerful tool -- thus being conducive to wide applicability, thus being widely applied, thus being a big part of many explanations -- is not the same thing as conclusively making up proportionally that percentage of the actual explanation... if that sentence construction makes sense. Especially in networks, and especially in systems with limited data.