It's not a zero-sum game because the stock price is tied to the value of the company. As long as the company increases it's value, the stocks can rise in price virtually infinitely (to match the value of the company) making it's owner more wealthy without decreasing the wealth of someone else.

Pare it down to the simplest situation Imagine you only have one company in the world. And it has 10 stocks. You own five and your buddy owns five. The two have you have done nothing but sit on the beach and drink beer all day, so your 'company' had no value.

One day you have an idea to do something. So, you design and create a new widget. Your buddy, who is good at sales, goes out and starts selling the widgets that you create. Now you have value, and the worth of your company increases. Eventually, you are selling three million dollars worth of widgets every year, making a profit of one million dollars each (one million in costs).

A zero sum game would mean that for every dollar in value you've created for your company, somebody else loses a dollar. That's not the case because the company itself creates value by producing some good or service that didn't previously exist.