The question of ultimate limitation to microscopic space-time description is the question about the inner structure of the particles, mentioned in the above quote.
As long as the inner structure is ignored, a particle can be treated as ''pointlike''. This is appropriate at a resolution larger than a few diameters of the particle (where the approximate diameter is determined by its scattering cross sections). But at a more microscopic resolution, the nner structure cannot be ignored without distorting the behavior of the particle, and a more precise description is needed.
Thus if the particle is an atom, the limitation of the pointlike description is due to the existence of electrons and nuclei. If the particle is a nucleus, the limitation is due to the existence of protons and neutrons; and If the particle is a proton or neutron, the limitation is due to the existence of quarks, etc..