I, too, have never seen the Two Ronnies sketch, but I really liked this a lot because it's just clever, clever writing. I'm also sad to say that I couldn't get through most of the linked Two Ronnies sketches because of the references that Brits would understand.
I agree with whomever said that the tension of having a breakup, a business deal, and a customer return transaction at the same time made things funnier than a date and a grocery list and I think it's because each person in their side of the conversation has a similar goal (to win the argument/deal) and so the conversations would flow that much easier.
Looking forward to next week!