Energy density is more a problem of materials. If you start talking GW hours it’s ~1GW from a ~38 ft tall and 48 meter diameter tank, even at $1,000 per ton it adds up. On top of that you need steam turbines etc.
Think of it like a scaled up, reversible refrigerator.
I'd like to know if they also have a 'medium temp' tank, since if they do, they can keep the temperatures of the hot and cold tanks constant, and just change the amount of molten salt in them. That in turn means the compressors can be fixed compression ratios, which will dramatically increase efficiency.
The paper suggests changing the pressure of the working fluid to adjust load, but I suspect it is hard to design a turbine to be efficient at a wide range of working pressures, so instead they'll end up with many parallel turbines, and just switch some off to get less energy produced.