Is it zero sum? It seems net loss to me. Just consider the lifetime of a single share. Company IPOs and someone buys the share for $100. The share may pass through thousands of hands, some at a profit and some at a loss, but eventually that share value goes to zero and the net loss over the lifetime of the share is its IPO price. It's only possible to have a net gain if there's dividends paid out. Is there some other mechanism I'm missing?
I like where you're going with this but I think you're taking a big leap at "the net loss over the lifetime of the share is its IPO price". And not because of the "not every stock eventually goes to $0".
I also don't have a definitive answer however some things that play into the equation must be:
I think VWAP (Volume-weighted average price) also plays into how much money was made by people and how much was lost in aggregate. This specific share we are tracking along its lifetime might have exchanged hands a lot while it is going up and traded rarely during periods of decline.
Also the share could have been first purchased as a part of the options given to investors, employees, etc.