Water is a perfect medium to store sunshine as heat for a variety of reasons. First, in terms of BTU/weight unit water = 1, every thing else is a fraction.
Everything. And water is usable at temperatures easily achieved by simple technologies or smaller collectors. And as described in the article the water is directly usable as steam rather than pumping it through heat exchangers inside some other hot mass, which might lower the cost/complexity/maintenance issues for other systems.
Storing sunshine in a flywheel wouldn't be very efficient because PV panels are still pretty low efficiency, then you waste energy as heat turning the generator/motor that turns the flywheel, and again as the flywheel turns motion back in to electrons. I think this is called "round trip" efficiency.
Molten salt can store higher temperatures than water, but those temps are really outside the bounds of simple systems. If those temps are available within the design of a system, then sure, you can use it and then pump water through it to create the steam. And the energy density is about half that of water, as shown in my link above. But for large systems with large solar collection, then yeah maybe the higher temps available give engineering advantages that outweigh the losses, costs and complications.
As I understand the idea the point is to use a reciprocating steam engine of advanced design
(wiki page on the type), which could be built within the existing industrial base of reciprocating piston combustion engines. Not so simple, I suspect, as yanking the heads off a honda and converting it to steam but still easier engineering and machining than steam turbines, and very easily scaled. You could make an engine about the size of an ordinary portable generator engine, or you could make it the size of a big stationary diesel like the ones hospitals have.
Storing sunshine as heat is a good idea, if you have a way to turn it into electrons. I like the idea of this. Even if your hot tank is below boiler temperature, the idea in the OP article is to run it through some kind of flash boiler using a secondary source of heat (I could see natural gas as a good source for this heat) to raise the temp/pressure to working levels.
In general I like steam and would like to see it come back into wide industrial use. If we hadn't had good gasoline engines to burn a readily available and easy to transport fuel come into play we'd all be driving Stanleys today. In fact, late Stanley Steamers used gasoline as the fuel for their flash tube boilers.
Flywheels scare me, because they require immense RPM to have decent energy density. That means higher technology (metallugy and composites) to build it, complicated systems including magnetic bearings and vacuum pumps to make sure you're not wasting energy, things like that.