The ingenuity of their invention is that it makes the energy storage of a given m^3 of higher more easily. The problem with pumped storage on land is that the work done is V * rho * g * h with h the height you pump the water, V the volume of water, rho the density of water and g the gravitational constant. Storing 1m^3 of water (1Mg) at 1m gives 10MJ or 10/3600MWh, so you need to store 3600 tons of water or store 1 ton 3.6km above ground to get 10MW or some combination of both.
When you go under water the pressure increases and you have to pump against this pressure. The formula is (if I recall correctly) (P0 + rho * g * D) * V with D the depth under water and P0 atmospheric pressure. Ignoring P0, you would need a reservoir 700 meters above ground to store the same amount of energy in the same amount of water. A 700 meter water tower is harder to build than an underground reservoir.
But the tower solution doesn't need a concrete/steel pressure vessel capable of withstanding whatever the pressure is at 700 meters. Just a bladder would do.
They're in the Alps. Why not just put a bag of water uphill. Fill it using excess energy. Drain it to run a turbine.
When you go under water the pressure increases and you have to pump against this pressure. The formula is (if I recall correctly) (P0 + rho * g * D) * V with D the depth under water and P0 atmospheric pressure. Ignoring P0, you would need a reservoir 700 meters above ground to store the same amount of energy in the same amount of water. A 700 meter water tower is harder to build than an underground reservoir.