I think you’re supposed to think that “open on…” indicates a day, rather than a time, and the store is now open every day of the year, including Thanksgiving and Christmas, so the answer is always “yes.”
It doesn’t really work, because the person could be about to say “open on Thursday at 3 AM.”
The joke is that he’s stupid but thinks he’s so much smarter than the customers. You see this a lot if you read any forums or message boards where people who work in customer service jobs all complain about customers.
I concur with WW, although not as strongly with the conclusion.
Comics I Don't Understand 
I think you’re supposed to think that “open on…” indicates a day, rather than a time, and the store is now open every day of the year, including Thanksgiving and Christmas, so the answer is always “yes.”
It doesn’t really work, because the person could be about to say “open on Thursday at 3 AM.”
The joke is that he’s stupid but thinks he’s so much smarter than the customers. You see this a lot if you read any forums or message boards where people who work in customer service jobs all complain about customers.
I concur with WW, although not as strongly with the conclusion.