The argument that Santa is a thief provides nice irony to the traditional gift giving nature of Santa. The elaboration focuses on enjoying a coke with family and friends, which is a different argument than what I am getting.
You provided thorough evidence for the idea that Santa says the holidays are not complete without a coke. The thesis that Santa Claus is used as a means to promote the sell of holidays and more specifically, coke. However, I think we can dig deeper for a more telling thesis. Perhaps using the interaction of Santa and the little girl reflect something about parenthood in the 60s or whatever the era this ad is from.
You spend most of the elaboration talking about how the ad promotes the product, try focusing more on the traditions it is promoting as well. Like how the little girl stays up late to see Santa, and how he is trying to be stealthy but gets distracted. Think of what family values are shown by what is in the fridge as well. The turkey in the fridge is promoting this idea of consumerism on the holidays with a lot of food.