Event horizon is a pretty different beast than radius. If we define "density" of a black holes using event horizon instead of radius (black holes don't have real radius), then supermassive black holes are actually pretty "light". A black hole of the mass of our universe would have "density" of the universe, which is mostly empty.
In case that point happens to be false, I think his other argument still works:
- "data centers ... are spread out on the two-dimensional surface of the earth"
- if we tightly pack these data centers on the surface it will form a circle with area O(N) so distance to furthest data center is O(sqrt(N)). (sky scraper height is negligible)
Anyway, it's more of an interesting thought experiment than of any practical use. Nobody sane would estimate cost of generic "information retrieval" that mixes cost of ram/disk/network.