The next step has a little hand waving though. Man acts in rational self interest. huh?

I don't think they make quite that leap. The claim is something more like, "Humans act. Action necessarily entails a goal. Having a goal entails preferring certain states of the world over other states of the world. Therefore, humans have preferences."

Mises and Rothbard are quite clear that these preferences don't have to include self-interest and actors don't always succeed in achieving their goals. I think they both assume that people are self-interested and semi-rational, but don't claim that as being a deduced truth. They should have been much clearer about when they introduce assumptions like this though, as Swimmy pointed out.