The average American house on a basement will have something like 40 m^3 of concrete in its foundation. If all of it could be utilized, that's still ~12kWhr of storage capacity. Nothing to be sneezed at.
That doesn't seem worth it when you can fit that amount of storage in about 20 L with lithium ion cells (think a small PC case), or something like 40 L if you used sodium ion cells, which are looking like a new alternative.
Concrete offgassing of CO2 is already a big contributor to greenhouse gasses, so I can't imagine this battery version is improving things there. You'd probably have to wire your whole basement with electrodes to even access the stored energy.
OK then, so this is incredibly far from being near any real world application
I'd disagree with that, but we certainly need more info.
There are places on Earth where 300wh would be plenty and very far away from traditional power grids. Think like remote sensing weather stations or data collection stations. So a small solar panel could power these during the day and these supercapacitors would replace a wearable battery currently in use today.
We'd need more information how these perform under various temperature and moisture conditions.
A cubic meter is just a whole lot of volume for incredibly little power. A regular 80Ah car battery has almost 4 times the power capapcity as a cubic meter of this.
And the research team are now planning to build larger versions, including one up to 45 cubic metres (1,590 cubic feet) in size that would be able store around 10kWh of energy needed to power to power a house for a day.
Its not a replacement for lithium, but it gives some interesting information for developing future applications.