What are you on about? I genuinely don't understand your point. Of course they make money by selling pizzas, not something else. And they've figured the way to maximize that is by having a brand and a presence and own the customer relationship, thus people buy from then.
If they end up as just a pizza-api they have no moat and are trivially replaced by another api and bakery, and will make less money.
The original comment may be phrased clumsily. I believe the idea was that they do not want to make money by competing on a pizza market. That's the contradiction as old as the modern economy that it both relies on free market in principle, yet evolves naturally toward monopolies/walled gardens/fiefdoms.
Another contradiction at play here is that of inovation vs standardisation. Indeed, you could argue that dominoes' website is also a place where thay can inovate (bring your own recipes! delivery by drone! pay with tokens! wtv!) whereas a pizza protocol would slow down or prevent some inovation. And that LLMs are used to circumvent and therefore standardize the process of ordering a pizza (like you had user maintained APIs to query various incompatible banq websites; these days they probably use LLMs as well).
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.
Making money by selling pizzas? Maybe. Big chains make money by selling high profit items like drinks or fries or getting you to upsize. And a whole sales process and a/b tested menus and marketing to encourage you do choose the profitable options. They lose all that if an agent just makes an order 'large pepporoni kthx bye'. Probably fantastic from a consumer point of view, but lots of businesses are going to hate it.