The simpler answer is that Rothbard is wrong here. Not a statement about Rothbard in general, but on this particular point he’s off. There need be no preexisting “direct” value for money, where the value of money itself is artificially deemed as of some second-class “indirect” sort. The value of a commodity as money, because it more securely scarce (and portable, hard to steal, etc.) than an alternative commodity, is quite sufficient to make it valuable as money and thus to get it going as money. Enabling exchange, i.e. lowering transaction costs, is a form of economically useful consumption just as much as satisfying hunger, decoration, or some other “direct” use is a form of economic consumption. In the same way, a stock exchange doesn’t have to satisfy your hunger or make a good decoration or have any other “direct consumption” value, it just has to be good at exchanging stocks.
This is well explained here (interestingly enough by the guy who originally came up with the bit gold idea): http://szabo.best.vwh.net/shell.html