That doesn't sound right to me. If there's no air, then only black body radiation can be used to cool the data center. That means a massive radiator, a lot larger than a heat-to-air radiator+fan used on earth.
But geothermal cooling would be great on the moon too. Run a pipe 2 meters under the lunar surface and it is -21C.
I think the whole idea though is to make a low wattage space-stead so you can store copies of Moana out of reach of Disney cease and desist letters.
I would expect the regolith to be a poor thermal conductor. Not useful for heat exchanger
But for radiative cooling, vacuum with a clear view of the night sky is orders of magnitude better.