"...capitalists buy and sell money as though it were a productive
No they don't. They buy and sell currency, because the price of currency fluctuates (due to imagination and/or economic fundamentals) and so there are profit opportunities there.
Also, they are after liquidity, (i.e. holding money instead of physical capital), because liquidity enlarges the set of feasible economic choices that they can make (but since they have to eventually make some choice, we get to see some physical capital lying around after all).
Money per se is not productive (is just paper, or electronic bits) - but money is not just a medium of exchange, it is first and foremost a socially agreed upon store of value (socially, not intrinsically). This makes it (not just endows it with) purchasing power. People are willing to give up something that has, say, nutritional value, in exchange for an intrinsically worthless piece of paper (or for an even more useless electronic credit in their bank account) -and one can guess why.
Finally, all the financial world of "financial instruments", "derivatives", "futures" etc, is a bit about risk-management but predominantly, is a highly sophisticated betting market, beyond anything that casinos, horse races, soccer, etc have ever imagined or devised as regards betting. Here income and profits come from winning the bet, not because money is productive.