The authors mention a few examples of firms using big data methods to "set prices" and note that
What’s interesting about such centralized, algorithmic approach to price setting is how un-Hayekian it is.This is an interesting point as far as it goes, but a couple of things should be noted. Hayek's point about centralized decision making was about markets, not firms. If complete decentralization were optimal, then no firm need exist. Of course, such an absurd conclusion can't be drawn from Hayek's work.
Firms are obviously necessary (and Matt makes some good points about this in relation to Coase), but Hayek's point is about the markets in which firms operate. Decentralized markets generate prices that reflect the availability of resources needed for production and the tastes and preferences of consumers; these prices allow firms to provide what consumers want. The USSR was (largely) without the coordinating effect of prices, a key cause of its demise.
The second problem is the idea that these firms are "setting prices." Surely a price tag or the rate offered on the Uber app will in some sense be "set" by the firm. However, the firm has very little control over the price they receive because ultimately the consumer determines the equilibrium price to which actual prices continually move. The influence of regulations, competitors, and (perhaps most powerfully) the preferences of consumers will decide what price the firm receives. The firm can "set" any price it likes, but decentralized free markets ensure that these prices come to closely approximate the value consumers place on the product.