Buying a rental property is just exiting the previous holder too.

I would define it differently. If you are putting money in something with the hope that the price goes up, that's speculating. If you put money in something with the hope that it generates income then that's investing.

So buying stocks could be either one.

Thought experiment: suppose company C does a small IPO. I'm rich and buy all their offering.

Scenario 1: I hold all the stock for decades until I die. Under your terminology, I am the sole "investor". Fine.

Scenario 2: 1 millisecond after my purchase I sell everything I bought in the IPO to thousands of market participants. Under your terminology they are not "investors". I can't be an investor either, since I hold no more of the stock. Does the company no longer have investors?