The article does consider that option via splitting and storage of water, and then recombination via hydrogen fuel cells.
According to the article the mass of the storage vessels needed to store 2 weeks of pressurized hydrogen and oxygen are comparable with the mass of batteries you'd need, although I haven't done the calculations myself... Intuitively I would expect this to be more efficient than batteries though.
I think the point here is rather that power load at night can be much lower than power load during the day, if most of the energy is going to optional processes like making oxygen and/or rocket fuel.
According to the article the mass of the storage vessels needed to store 2 weeks of pressurized hydrogen and oxygen are comparable with the mass of batteries you'd need, although I haven't done the calculations myself... Intuitively I would expect this to be more efficient than batteries though.