It would be hard to conceive sparking the New Deal, aka the socialization of the American economy, as a sign of market forces working. Otherwise, the argument (as summarized) strikes me as quite plausible.Well, "good for the economy" isn't necessarily the same thing as "market forces working" not universally, anyway. But in any case, what's so hard to believe? Modern economies have a hard time working without a fair amount of regulation, and the New Deal provided exactly that: the SEC to ensure transparency in financial markets, the FDIC to restore trust in the banking system, unemployment insurance and a minimum wage to provide at least a minimal buy-in to capitalism from the working class, and much else. The New Deal may have had its overreaches, but 70 years later I think everyone not to Tom DeLay's right agrees that moderately regulated capitalism works better than unregulated capitalism, and that framework was what the New Deal provided.
In other words: yes, the overall result of the New Deal really was to strengthen markets, not weaken them. After all, Bill Gates is richer than John D. Rockefeller ever was and the worst recession we've had since World War II would be considered a mere inconvenience by our great-grandfathers. Seems like markets work pretty well these days.