You are correct that economics is not a zero-sum game. Investors pay money to buy stock in a company, and that company tries to create value for its shareholders. If they succeed, then it's a positive-sum game for the shareholders, employees, and customers. When enough companies create value, then the economy grows, and the economy is a positive-sum game.
However, this article is not talking about the economy as a whole, or about investing, but about high-frequency trading. And trading is a zero-sum game. Value is not created in the 40-milliseconds between trades, and for everyone who makes money trading, someone else is losing money.
There's a good explanation of this in an article by Henry Blodget.
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"There is no distinctly American criminal class except Congress." -- Mark Twain