Not strictly, no, but there are limits. I think most people will agree that it's not a democracy when a single person controls all of the votes (dictatorship),

Not strictly, no, but there are limits. I think most people will agree that it's not a democracy when a single person controls all of the votes (dictatorship), or when a small group with usually-aligned interests controls a majority of the votes (oligarchy). That said I think you've helped a bit with my confusion here. The point where it moves from democracy to something else is obviously not clear -- so probably the people who consider the market system to be democratic just draw that line differently from me.