How does the purchase of shares on the secondary market benefit the issuing company?
First, the stock does represent a share of ownership and if you have a different interpretation I'd like to see proof of that. Secondly, when the IPO or secondary offering happened that put those shares into the market int he first place, the company did receive proceeds from selling those shares. While others may profit afterward, it is worth noting that more than a few companies will have secondary offerings, convertible debt, incentive stock options and restricted stock that may be used down the road that are all dependent upon the current trading share price in terms of how useful these can be used to fund operations, pay executives and so forth. Third, if someone buys up enough shares of the company then they gain control of the company which while you aren't mentioning this case, it is something to note as some individuals buy stock so that they can take over the company which happens. Usually this has more of an overall plan but the idea here is that getting that 50%+1 control of the company's voting shares are an important piece to things here.