The only moving part right now is the fan. That's needed because even a small amount of forced air flow greatly reduces the size of radiating fins needed to transfer heat from the system to the outside. Any compact fridge also needs a fan.
The computer needs to be cooled, but not below ambient temperature. The latter is where refrigeration enters the picture.
Any compact fridge also needs a fan.
I seem to recall that the absorption fridge in our old VW camper had a fan w/thermostat on the heat sink on the back of the fridge. A common mod was to put a bigger fan on it to improve efficiency. (W/o looking it up, it might not have had an OEM fan, and the mod was to add one, details are fuzzy.)
So, depending on circumstances, the fridge might not be completely silent.