I don't think that's true at all - it seems like Finance, Fashion, and Politics people are the richest in general, with geeks coming tied for 3rd or even 4th overall. Of the richest (known) 25 in the world [1], only 4 or 5 can be said to be "nerds", with some financiers and magnates in the tech industry doing fairly well also. The rest are all financiers, inheritors, politicians, etc.
I think you are using a pretty narrow definition of the word “geek” - and I would probably classify 7 of the top 10 of having some level of “geekiness”.
They are just different kinds of geek - Warren Buffett is a geek, just a “securities-pricing geek” rather than a “tech-geek”
You are talking about private wealth held in things like bank accounts, etc. These are always subordinate to the actual sovereign owners of the property. I think those who can ultimately control final disposition of resources are far richer.
The Medicis actually ran Florence. If you're wealthy in Russia or China or the USA today, you don't actually get to decide what happens with your biggest assets, push comes to shove, that's up to Putin or Xi or the CIA.