The cycles for air liquefaction and separation are highly optimized, but the basic idea is to compress air, cool the compressed air back toward room temperature, then send it through an expander (a turbine, say), converting much of its remaining thermal energy to work. This leaves the expanded gas colder than when you started.
He essentiallt states that you can only get a certain maximum % out of exnapsnio engines if you expand them to absolute zero in a vacuum.
Since you expand to room temperature and pressure, the equation determines that efficiency. That is why car engines are 35% or efficient. Specialized constant speed diesels a bit better and turbines close to 60%
I think in computing the efficiency, the comment above may have been to the work generated in cooling the air, but not the work generated from the boiling of the liquid air. Also, I wonder if separation is necessary in the application referred to in the OP, since they're not trying to purify liquid nitrogen, but just store energy in the temperature differential. If they're just going to boil it back off again, they might not care about removing impurities.
