If we take that 876 million cubic metres of water from his example and pump it to, say, lake mead (also in his example), the total change in gravtiatonal energy is
m = 876 10^6 m3 water = 876 10^9 kg
g = 9.81
h = 375m lake mead
mgh = 3.22 10^ 15 J = 895 GWh
If my calculations are correct, the energy cost of pumping the water exceeds the cost of desalination by far. Now obviously IRL all that water wouldn't go to lake mead but a back of the envelope calculation shows that the water pumping costs shouldn’t be ignored.
It would probably be better to use desal for providing coastal cities with 100% of their water and simply reducing the amount that we pull out of the rivers in the first place