They're taking saltwater from brackish aquifers inland, not pumping it from the sea. In terms of pumping costs, it's no different than their current sources of water that are pumping out of the Edwards aquifer or other fresh groundwater sources.
If you assume more than enough energy, likely from advanced solar (a big assumption, but we haven't been to the future yet), then pumping water can serve as energy storage in addition to more direct use of water.
We do the same thing with oil, I don't see why water would be any harder. Though granted, oil has higher cost and different outside factors than water, so I really can't make any 'is it economical' claims.
Where do you get the saltwater high above sea-level?
I think they are talking about pumping desalinated seawater over a thousand miles inland.