It seems like either this is describing an additional energy storage/extraction method that’s possible with these systems. Either to improve the efficiency or something that’s actually far more efficient than utilizing kinetic energy compressed air can create.
It’s kind of like saying the water in a hydropower plant doesn’t store energy. The turbines aren’t extracting energy from the water itself. They’re extracting energy from gravity acting on water. It doesn’t matter if the water is nearly freezing or nearly boiling, it has roughly the same amount of hydropower available.