To me, it's like this: If you enter someone's house and they ask you not to smoke, out of courtesy, you don't smoke in their home. It would be rude to, right? Well, this is DCL's home, so to speak. They make the rules. We are guests on board their ships. They request that people (men, women and children) not wear shorts to dinner. This seems like a reasonable request. They're not requiring women to wear skirts or dresses every night, or men to wear 3 piece tuxes every night. They're asking that people not wear shorts to dinner. As in the above example, it would be rude to do otherwise. So, you must decide for yourself if that's a rule you will follow or not. Many people don't follow that rule, but that doesn't necessarily make it OK.
Will they let you into dinner wearing shorts? Absolutely. Will people look at you funny or roll their eyes at you? Possibly, but you may or may not ever even know. And if another guest were to ever say anything to you about it, that's shame on them - not shame on you. Nobody on this forum can tell you whether you're going to feel comfortable wearing shorts when the majority of people will be wearing pants or possibly even more dressed up than that. You might feel comfortable; you might not. We don't know you so we can't tell you how you will feel in that environment.
All we can say with certainty is that DCL has asked that guests please not wear shorts to dinner.