The numbers in the article look very much like a power-law distribution. Power-law distributions are often the result of self-organizing phenomena, so it might be that Harvard actually doesn't do anything special or explicit compared to other elite universities. It's probably just the result of an initial lead coupled with a network or snowball effect.
[Added: Solipsist made good comments that partially account for the phenomenon, and Douglas_Knight pointed out that the figure of $200m+ below should be $30m+]
This article reports that Harvard has 2,964 alumni worth $200+ million, with a total wealth of $622 billion. These figures are staggering:
Note that Bill Gates "only" has ~$75 billion and that Mark Zuckerberg "only" has ~$30 billion, so that they don't account for Harvard's decisive advantage over other universities.
What is going on here? Why would Harvard come out ahead by such a large margin? Its acceptance rate is smaller than those of Stanford, Yale and Princeton, but by no more than 25%. Moreover, this has been true historically
One can ask a similar question of University of Pennsylvania, which is significantly less selective than Yale and Princeton, but has a decisive advantage over them.
Some possible explanations for the discrepancy:
Regardless of which of these explanations hold, there remains a question of why they would hold.
Is Harvard a better choice than other universities for students who aspire to be wealthy than other top schools?