They're talking about the sales experience that a pizza API would completely sidestep.

The big national pizza chains don't offer good prices on pizza. They offer bad prices on pizza, and then offer 'deals' that bring prices back down. These deals, generally, exist to steer customers towards buying more or buying higher-margin items (bread sticks, soda, etc).

If you could order pizza through an API, they wouldn't get the chance to upsell you. If it worked for multiple pizza places, it would advantage places who offer better value with their list prices.