They highlight less the advantages from breeding, than other advantages of the molten salt design, like not needing a lot of cooling water, which allows this reactor to operate in the Gobi desert, the possibility of replacing the fuel without halting the reactor and various safety features.
The use of water for moderation is one thing, the use of water for cooling is another thing, even if in many reactors water is used for both purposes.
A reactor can be moderated with something else than water, e.g. graphite, but it may still need water for cooling.
The amount of water needed for cooling is much more than needed for moderation.
So there is no doubt that many "non-water moderated reactor designs" still need copious amounts of cooling water.
Any "non-water moderated reactor design" that does not have liquid fuel, i.e. it is not a molten-salt design, must have a cooling fluid, though the fluid in the primary cooling circuit may be not water, but something else, e.g. molten metal (e.g. molten sodium) or supercritical carbon dioxide.
I believe the point was that non-water moderated designs typically operate at higher core temperature than LWRs, so they can reject waste heat at higher temperature (or reject less waste heat per unit of electrical energy produced), and that makes rejection to air more practical.
A very high temperature reactor might even be able to work with an open air Brayton cycle system, which would allow heat to be directly exhausted in that air stream. It would probably still need an in intermediate heat exchanger so the air wasn't being irradiated with neutrons.
No, because it would require very high temperature. The air coming out of the compressor of a gas turbine would already be hotter than the water/steam coming out of a LWR. It would likely involve a core temperature of around 1000 C. The turbine inlet temperature of a modern jet engine is at least 1500 C. There would likely be thermal NOx production, so post treatment of the gas might be necessary in an open cycle system.
Nuclear reactors don't need a particularly big amount of cooling water.
The thermodynamic cycle needs a cold source though, and it's most commonly water. This doesn't depend on the reactor design and this is equally as true of coal plants.
As long as you are making electricity out of a thermodynamic cycle, you need a heat source (be it a flame or a nuclear reaction) and a cold source.
As the reactor is operating in the Gobi desert and China claims that its main advantage for them is exactly this possibility of operating in the inland arid areas of the country, unlike their current reactors that must be installed only close to the sea, in the part of the country with abundant water, they must have a solution for the cold source that does not involve water.
Perhaps they use as a cold source the underground soil, though the soil thermal conductivity will limit the amount of power of the reactor. This reactor has a modest power, which could be explained by this constraint.
If the reactor is as safe as they claim, the moderate output power per reactor could be compensated by installing many such reactors.
> As the reactor is operating in the Gobi desert and China claims that its main advantage for them is exactly this possibility of operating in the inland arid areas of the country
This is mainly a feature of the reactor being small. If you don't have much heat to dissipate, even air cooling becomes feasible.
> unlike their current reactors that must be installed only close to the sea, in the part of the country with abundant water
In reality even current water-cooled reactors can be pretty efficient in terms of water use if you design the cooling system with that in mind. See the Palo Verde Nuclear Generating Station in Arizona.
> Perhaps they use as a cold source the underground soil
I'm not sure this would work, as you'd be storing heat in the soil without a real heat drain so the yield of the plant would decrease until it reaches zero.
For small reactors air or radiative cooling are an option though.
