It feels like your calling the idea of economy in general a zero sum game. Can you elaborate?
An IPO takes some money out of the market, to the pre-IPO investors in the company, but a much bigger impact is made by dividends.
Here's a thought experiment for you: A company, A[1], IPO's. It's investors take some cash, the rest goes into A. A is a fantastic success and eventually grows to be the largest company in the world, market-capitalization-wise. Then, like all things mortal, it begins to slide into obsolescence, obscurity, and eventually bankruptcy and dissolution. Throughout its lifetime, following the best advice of economists[2], it never pays a dividend.
Anyone investing in A's stock is playing a quintessential zero-sum game: they're betting A will go up before it goes down permanently.
[1] No offense to Agilent.
[2] The goofy "double taxation" argument. The "it's no longer a growth company" argument (causing an immediate collapse in A's stock price). Etc.
Rich people also invest in many other things that do not further sustainable growth and, as we can see from many corporations, many of them actually hoard cash or invest in bonds (which just fuel unsustainable consumption - hardly the growth that seems beneficial long term)