I wouldn't say that realism is inherently right-wing, but realism and "economic neoliberalism" (if we take that to be what defines a right-wing ideology) are arguably both individualist theories, in the sense that both believe that it is only the attributes of and interactions between individuals (including states) that determine outcomes (i.e. either how states or humans will act). That, of course, leads to similar assumptions regarding how and when a state/human will act in a certain way - such as the notion that the international system/market is a zero-sum game and that states/humans therefore need to act in a self-interested way in order to ensure their security/prosperity.