Theoretically, what would happen if everyone tried to sell their stocks in every other company in the world and simply try to buy Apple stock because of it's performance? What would happen to the stock market? What would happen to all those sell orders that couldn't be fulfilled because everyone is trying to sell? Since no one is buying your GE stock because they want to buy Apple... what happens to the money?
Zero sum means there's a constraint on the game such that all gains are offset by equal losses. If someone gains X, another person loses X, and X + -X = 0.
Here, there's no such constraint. The stock market has been zero-sum for specific lengths of time in the past, but it doesn't have to be. In practice, it's not overall. Because economies grow and people become more productive, the value of the stock market grows over time.
In practice, there are going to be winners and losers, but there's no constraint saying that has to happen. In fact, there's more won than lost in the stock market overall, so it's not zero-sum. The sum is greater than zero.