I'm going to expose my ignorance here, but I thought mAh/Ah was not a good measure for comparing storage of quite different devices, because it doesn't take into account voltage. This is fine for comparing Li-ion devices, because they use the same voltage, but I understood that using watt-hours was therefore more appropriate for apples-to-apples comparisons for devices with different wattages.

Am I missing something? Does the CPU/GPU/APU doing this calculation on servers/PCs run the same wattage as mobile devices?

No you are completely right. mAh is a unit of current over time. Not power.

The proper unit is watt hours.