Consider (abstract) agriculture. You buy seeds, that's a "zero-sum" transaction, plant them, wait for them to grow, pick the harvest and sell it in another "zero-sum" transaction. Both your transactions with the market are zero-sum and yet... :-)

Yes, but you can't plant stock options in the ground, and in fact you can't really do anything with them other than selling them or keeping them and cash the dividends (assuming that you don't buy enough shares of a company to gain control of it).

Since different people can assign different utility to cash and can discount future utility differently, it is possible that a transaction is positive sum: e.g. consider an old person with a short remaining life expectancy selling all their stocks to a young person. But at the level of large investment funds and banks, these effects should mostly cancel out, therefore the stock market is approximately zero-sum (up to events that alter the amount of available stocks, such as defaults, IPOs and recapitalizations)