"zero sum: relating to or denoting a situation in which whatever is gained by one side is lost by the other."

The data from the Fed show great inequality which can be expected from a zero-sum game. Another example check how under develop DR Congo is in the electronic age, while hardware (and to an extend software) companies are some of the most valuable companies, they all source raw materials from Congo.

Inequality is possible in a non-zero-sum game. It's just as possible to have an inequal non-zero-sum game as it is to have an equal zero-sum game.

Capitalism isn't zero sum because at its core principle are transactions, which are inherently non-zero-sum.

Its like chess in that white has an advantage because they get to play first. The rich get richer because you need capital to efficiently participate in capitalism and it has a compounding effect. It than becomes a zero-sum game where the poor are trying to play catch up with the rich. For example if you start an innovative company the rich can simply buy it or start a competing company that is hard to compete against because of their resources.

I'm sorry but what you are describing is not what a zero sum game is.