First, my apologies for the delay in responding. I just returned from vacation without technology.
Austrian Business Cycle Theory (ABCT) is built-up from, and hence integrated into, general price theory whereas neoclassical business cycle theories (NBCT) are not. Technically, I don’t think NBCT contradict general price theory. As the neoclassical economists see it, the two theories are trying to answer different questions. General economic theory explains the array of prices and allocation of goods whereas BCT explains booms and busts in the overall economy. Neoclassical economists typically assume that aggregate demand is a primary causal factor in generating booms and busts. Aggregate demand plays no role in general economic theory.
In the quote, Rothbard is highlighting the underlying difference between the Austrian approach and that of the neoclassical school. For neoclassical economists, economic theory requires formulating a model for each and every phenomenon they wish to analyze. Each model estimates the quantitative magnitude of effect produced by its cause and is tested by empirical evidence of the phenomenon at hand. They see no reason to investigate how the various models relate to each other. For Austrian economists, economic theory requires discovering the conceptual structure of human action. Because this is done by logical deduction from basic facts about human action, the entire edifice must hang together.