The year 2018 may be remembered as the time when the big pizza companies of America picked sides in the great robot-car race.

On one side, Domino’s Pizza Inc. doubled down on a partnership with Ford Motor Co. earlier this year, saying it would be part of the auto maker’s test run for how driverless delivery vehicles would operate in Miami. The two conducted a short test of pizza deliveries in Ann Arbor, Mich., last year.

The...