There's probably a much greater amount of energy lost from conversion to liquid form and stored and converted back into usable electricity from steam generators. I believe the article mentions it but it likely has better long term storage than batteries as well. The equipment required for the 'air' battery would have a longer lifespan and be cheaper to repair then a massive battery bank. On top of that batteries aren't exactly the most 'green' thing to produce, so from a carbon footprint perspective, I imagine the air battery is much more efficient.
It's not of course but for long term storage the capital costs of the storage are more important than the the round trip efficiency.
> This cannot possibly be more efficient than lithium batteries...
It really depends on what you perceive to be efficiency.