I'm surprised that, somehow, the article barely even touches upon the question of bandwidth. Terrestrial data centers often have hundreds of gigabits per second of transit - how much bandwidth would be available to this lunar data center, to what endpoint, and how reliable will that be? (Would one of these permanently shadowed areas of the moon even have line-of-sight to the Earth's surface, or would it have to be relayed through a satellite?)
The transit is even worse than that, right? The moon orbits the earth so at different times of day it is over different parts of the earth's surface. So the route is not only constantly changing, but sometimes you have to go around the entire earth (either via satellite relay or fiber) and then cover the distance from the earth to the moon on top of that.
It's hard to imagine any scenario where this proposal really makes sense.
If you have a problem that requires and hour or a day to compute, then spending fifteen minutes for data transfer up and down (particularly in the face of lowered costs) is often a profitable trade. Movie studio render farms are a classic example of such compute jobs. Weather or geological resource prediction could be another. There are many such high-compute jobs in practice.
Not only are those jobs relatively rare, but they also require a lot of hardware and a lot of power. Both of those are going to be in short supply. (Solar power requires sunlight, and the target locations are deliberately in shadow.)
