You are carrying fuel and using oxygen from the atmosphere to combust it. When it's hot, it's a gas. By simply cooling it and recovering most of it, you are potentially left with more mass than you started off with... and Oxygen is relatively heavy.
The fine article shows them lowering a container from a crane. I'd love to see them connect the crane to an electric generator and actually regen the potential energy of the container into electricity.
Even more efficient might be raising another container at the same time in a (mostly) balanced manner. Then you don't have as much loss from conversion/storage.
Fun fact: many inclined elevators work this way :)
This idea of extracting water from air keeps coming back, but every time someone tries it, they learn of the same thermodynamic limits. It is extremely energy-intensive to extract water from the air, and it only really works if the climate is humid enough that there is water in the air to extract. This is exactly what a dehumidifier does, and the off-the-shelf version you can buy at home depot is no more than 5-10x worse than the thermodynamic limits - those generate a pitiful amount of water for a lot of energy intake.
Do we even need to extract the water? The point is to capture weight, and the only reason to liquefy the water is to store it more efficiently, by volume.
Storing higher humidity air doesn't sound very efficient, storing liquefied humid air sounds like a disaster waiting to happen, and storing compressed air sounds like an unnecessarily complicated alternative to just compressing the hydrogen.
You're both missing the forest for the trees, when the airship is electric obviously you don't have to add ballast while flying because you don't have to compensate for burnt fuel.
That seems like it would be really bad for energy efficiency: now you need batteries large enough for propulsion during the whole trip, plus extra for extracting water vapor.
Why not just take on some liquid water at the destination when you drop the cargo?
Because that's less flexible and there may not be water at the destination in the first place. That said, Flying Whales are trying to do exactly that, because ballast tech just isn't capable enough yet.