Here's the research paper the video references. They got 65% efficiency, which is pretty good, but a far cry from 90% of a lithium powertrain made this decade.
The paraffin heat exchanger is clever, but it's a flammable coal/oil product, and phase-change thermal storage is notoriously tempermental outside a lab. The thermal-to-electrical-to-thermal recuperation cycle is likewise brilliant, but I think it misses the core appeal of pneumatic energy storage: compressed air is fundamentally low-tech.
Being low-tech means that it makes grid-scale storage accessible on continents that lack the engineering manpower or natural resources to set up domestic battery production or baseloads like nuclear and geothermal. After all, if renewables keep getting cheaper, who cares about storage conversion losses? Just build a little more peak capacity.
I'm also personally fond of the idea of using pneumatic storage for industrial centers that currently use cogen/CHP, because the waste heat could be used directly instead of having to be recuperated.