So running a store is also a zero sum game. Because for some reason we're also including money "from the outside" in the sum.
Running a store is different. When you run a store, you are buying product and selling it for a profit margin. Tangible goods and services. You staff people for a certain wage and provide services for a higher hourly surcharge.
The stock market is like running a store where you sell iPads, but nobody opens and uses the iPads. Instead, you sell iPads to other stores, and then use that money to buy iPads back when you think they're undervalued and can be sold again later next week for more money. Someone in this might get their hands on more money by other operations (i.e. actually selling iPads to customers) and buy more iPads from the supplier (new stock) or from other stores.
Trade provides a comparative advantage, where one party can provide one economic service cheaper than another party, and vice versa. For example: consumers can't build iPads cheaply, and manufacturers can't open direct retail outlets cheaply. Thus manufacturers use ecommerce and shipping, as well as third-party retailers. Because of the comparative advantage each participant has over others, the total wealth of this system is greater than the wealth of only individuals accomplishing the same: less labor and capital and energy and other resources are expended to get the same result.
The common argument for the stock market NOT being a zero-sum game is that share prices can be bid up without introducing new money. Unfortunately, this ignores the fact that you allegedly have $5000 of stuff to sell, but everyone together has only $500, and thus if you actually tired to sell all of that stuff you would eventually end up selling it all off for $500, in the process some of it likely becoming worthless.
This argument, thus, ignores the whole of the market. It's the same argument as "I am rich because I buy lots and lots of shit I can't afford on my credit card": you're making the payments, but you're perpetually in debt you can't pay off and thus you are poor. That you just got another car loan for a $60,000 Jaguar is immaterial, since you still only have $1000/mo and you have a 40 year mortgage letting you pay $150/mo on that jag by some fantastic manipulation of the banks.