The reason being people will actually stop ordering Domino's if they're upset at a mistake in an order. Even something as silly as not getting ranch dip you paid $0.50 for. Making it up to them with a free item way more valuable than the mistake almost made the customer feel guilty. After using their free pizza credit, a customer was almost guaranteed to order Domino's again within 2 weeks, and would generally order twice as often as they normally would for the rest of the year or longer.
My very first delivery ever, I opened up the heatbag and their whole order slid out and fell onto the floor outside their front door. Maybe still one of my most embarrassing moments ever, I was sure I was going to get fired. When I told my manager about it, he said "This is going to be more powerful than a hundred TV commercials"
Oh, and they have all your orders and previous free credits saved in the computer system that handles orders, tied to both address and phone number (or online account). So if you tried taking advantage of this thing they would just permanently ban you from ordering from our store. This only happened once or twice in my couple years there.