Your citation is rather out of date, it neglects to analyze, or even mention by name, save as an tacked on note, the critically important Denisovans. Science changes (as you have observed) so citing current work is critical.
My thoughts are that there have been five extinctions and we are hell bent on creating the sixth. What is your question?
It takes a long time to evolve a species, even longer to evolve an entire ecosystem, and all can be snuffed out in a moment by a change of sufficient magnitude. This creates a lot of empty niche space and each evolution is followed by comparatively rapid (still quite slow in absolute terms) expansion of the number of new species and the open, low pressure niche space permits novel experimentation with regards to novel species and adaptations.
Additionally, your assumption that an extinction of 96% means that not only the extant species died, but that it did so without the benefit of producing evolutionary decedents may be a dangerous assumption, even when viewed at higher taxonomic levels. For example, it is safe to say that within the next 200 years, despite the fact that the human population continues to expand, 100% of the extant human genotypes will have gone extinct.