The Theory of the Firm is an interesting and foundational one, but we should be careful to define "free market" in this context. A labor market still exists inside, outside, and between firms. Firms are simply organizing small aspects or chunks of it. They are both part of, and subject to, the broader labor market.
ToTF is actually a very interesting framework through which to evaluate the "Sharing Economy." It suggests that transaction costs for certain goods and types of labor have been lowered to the point where freelancing / ad hoc exchange makes sense. But there is still an organizing force underlying these pockets of the market. Lyft and Uber haven't eliminated the previously existing firms in the taxi marketplace. They've organized the market more effectively, and in some cases, they've lowered transaction costs for the marginal labor supply who otherwise would not have entered the market. They have also increased and aggregated demand, further incentivizing latent supply to come online. The story of Lyft and Uber is largely a story about how technology made inefficient markets a lot more efficient.
I'm not sure I see the connection between these companies and the plight of the middle class in America. That's where the author of this piece loses me. It's almost as if he's covering two interesting, but tenuously related topics in the same piece. The "hustling" imperative is an interesting one, however, and he's on to something with that.