You'd be giving money to the company if the shares actually came from them. If you're buying on an exchange ... you're exchanging cash for shares with the counterparty almost never ever the company itself. The company is not acting as a market maker on its own stock, for example. The only way the company would benefit is if the purchase increased the ask price so that at the end of the day the price per share was higher.

As you say, someone else has already given Chevron that money. Buying Chevron shares from “some other gambler” does not give Chevron money.