I haven't read the book, and only have a high school knowledge of economics, but that seems fairly intuitive to me.
Wealth is effectively "liquid power" and "power" is the ability to get other people do to what you want. One of the absolute most obvious things you'd want them to do is... give you more power.
So I think it's a pretty natural outcome that, absence other forces, any power imbalance will tend to magnify over time.
Times in history where the entire economy is growing very fast basically mean new power is raining down on all people uniformly. That will tend to reduce disparity in the same way that adding the same positive number to both the numerator and denominator leads to a fraction closer to one.
Of course, this simplified model treats every person as an island. Where the story gets more complex is when you consider people working together in a group. And I think through most of history when you've seen power imbalances get reduced, it's because you've seen people work together to form groups that have greater power than the smaller number of individuals they are pushing against.
One of the things that really scares me about the US today is how much we've culturally lost that ability to organize and work together. And, of course, the small number of increasingly powerful people and groups like it that way, as they always have.