I expect the same thing will happen here as happened when Google X said they were looking into space elevators. They'll conclude it won't be feasible because of already-known engineering challenges for which there are no technical solutions that are economically viable. The big barrier for space-based data centers is heat exhaust, which does not work well in space and typically requires enormous radiators. They allude to this in the paper but just gloss over it.
Has anyone ever deployed a heat pump in orbit to increase the radiator temperature? T^4 is a pretty steep curve. If your usual rejection temperature was 77 C / 350 K, and you could bump that up to 227 C / 500K, your radiator goes down to ~1/4 of the required area. But then you need more solar panel area to power the heat pump. And 1/4 of the area is only ~50% smaller in linear dimensions. Maybe it doesn't pencil out. Maybe instead of powering the heat pump with PV panel electricity, it is mechanically driven by a heat engine driven by concentrated sunlight. 1000 K warm end, and 500K cold end. But then you need to dissipate the waste heat from the engine as well. Fun to think about anyway.
Heat pumps are used a lot in space already. They do not address data center scale heat removal.
What is a good rejection temperature to use for medium earth orbit? Assuming you would orient your radiator normal to the incoming light from the sun, and normal to the earth-shine/earth-radiation. And in the shade from your PV panels. Is 50 Kelvin a reasonable temperature? Then you could radiate 1 GW of thermal energy at 350 K using a 2.5e6 m^2 surface (assuming 0.9 for emissivity). That is a square about 1.55 km on a side. Maybe reversible computing is step one in this plan.
Interestingly enough, to get 1 GWe, using 30% efficient PV panels and assuming 1360 W/m^2 insolation, you'd also need ~2.5e6 m^2 of PV panels.
Ah, for a radiator, you can use both sides; one side exposed to the solar system north, and the other side facing south. So the 1.55 km on a side gets reduce by a factor of sqrt(2), to 1.1 km on a side.