I think there a physics problem there. The efficiency is way worse than charging almost any type of battery. So unless material for any type of battery becomes completely unavailable (including say Iron and sulfur or lead), the power free and you manage to build your Air Liquifier with less resources than batteries it will always be a stupid way to spend resources.
OK, I have thought about this a bit (I have worked on gas liquefaction plant design), and I do not believe this claim.
70% is about the maximum thermodynamic efficiency of any heat engine operating between -190 degrees and ambient. And the best efficiency you can expect in liquefaction, in a very complex and large plant, is circa 50% (1). Combined with storage losses, I think the overall cycle efficiency cannot be more than 25% or so.
Happy to review and comment on any back-up to their claim.
