Might come down to things like, how efficient are cranes & conveyors & so forth, vs water pumps & hydro generators. The nature of each material leads to different techniques which could have very different efficiencies.
The article does mention that they expect to use 1/6th the cement of construction concrete.
This paper https://www.nature.com/articles/s41893-017-0009-5 gives an idea: 2 Gt of water per 21.3 Gt of not-water.
Assuming perfectly dry concrete (and none of the water converting to not-water mass, both of which I believe are counter-factual), that means a 2130 kg block of concrete would have needed 200 kg of water. Pumped hydro, assuming identical efficiency, would need all 2130 kg of water.
That article does go on to cover the water footprint, but what troubles me is that they switch units, and report it as 16.6km^3 of water. Which seems like they're trying to obfuscate the results (they have obfuscated them, whether that was intentional or not is another question).
That's all the water for all the concrete. Which for a hydroelectric perspective, is about 5% of the volume of water behind Grand Coulee Dam, for all the concrete we currently make every year. So maybe concrete blocks make sense for power.
True, though the paper makes a point, early on, that much of it is used in producing the aggregate, and the article makes a point of (potentially) using recycled/discarded aggregate, which would incur no additional water consumption.
> report it as 16.6km^3 of water. Which seems like they're trying to obfuscate the results
That's a remarkably harsh characterization, especially since that was parenthetical. The main reported amount was 16.6 × 10^9 m^3.
With water having the convenient density of 1000kg/m^3 (1 ton/m^3) and 10^9 being equivalent to the SI G prefix (both facts which one reasonably expect a reader of a physical sciences journal to know casually), it seems hardly obfuscatory. I'd attribute, instead, a change of units to a desire to compare it to household use, later in that paragraph, which is more typically measured by volume.
Although for commercial concrete block of 2130kg, that would, indeed, change the amount of water to be 1660kg from my original 200kg. However, I'm fairly confident that the ability to use 1/6th the cement combined with not needing any particular aggregate (even recycled) will bring the number for the article's application much closer to the smaller one than the larger one.
Which it should be - IMHO, despite the material, both systems get very similar techniques, at the core in both cases you have the loss of a motor+generator pair plus the friction of your mechanical system.