Case can be short for suitcase. A suitcase is a case with a handle and a hinged lid. It's considered luggage. To "make a good case" means to "make a good argument" for something. So, here the luggage salespeople have to be convincing in getting you to buy their luggage by creating a good case. The joke is centered on the word "case" and how it can be used to describe luggage, but also a persuasive perspective. 
Luggage salespeople have to make a good case for you to buy .