Why wouldn’t the steam turbine cycle or pressurized water in the primary circuit work?
Terrestrial nuclear reactors need a lot of water on the tertiary circuit but on Mars that can just dump into the ground instead which isn’t possible on Earth. The primary and secondary circuits are closed loop and don’t need so much water that it would be prohibitive, at least not compared to the difficulty of getting everything else to the planet and assembled.
I don't think dumping heat into the ground would work for any meaningful amount of time - both on Earth and on Mars the dirt and rock are not a very good conductor of heat, so you would quickly heat up your local "heat island" in the ground soon loose the temperature difference to run our heat engine on. Might work for pulsed operation where you wait for the affected area to cool down, but I am skeptical, given that a similar system is used for heat storage on Earth and it can take months to years for the temperature to return to natural values.
Most likely you would have to use air cooling, with lots of fans to push the thin atmosphere through massive heat exchangers. The overall lower atmosphere and general ground temperature (due to Mars being less heated by the Sun) should help offset this somewhat compared to cooling a reactor of the same power output in the vacuum of space.
There already exist better solutions for the primary circuit than using steam, e.g. using supercritical carbon dioxide in a closed cycle. This allows the operation of the reactor at higher temperatures, while also increasing the efficiency of the heat transfer in the heat exchangers, which increases the overall energy efficiency. Moreover, this also greatly reduces the size of all components (which however must operate at much higher pressures than with steam, because that is the reason for the great reduction in size).
Making very big heatsinks to radiate all the heat from a nuclear reactor will not be a problem on Mars or Moon, as long as the metal, e.g. aluminum, is extracted locally. One will have no neighbors and no need to buy real estate, so any amount of land area can be used without restrictions.