The story explores what happens if we take seriously the imperative that people should be equal. Not, it should be noted, what happens if everyone has equal opportunity, since that, after all, will lead inevitably to unequal outcomes; nor what happens if everyone is equal before the law, since that too will allow unequal outcomes. It explores, rather, what the world might look like if the state took it as one of its duties to ensure that no one had any more of anything than anyone else.
Is it unfair that some are smarter, more beautiful, more talented than others? Is it especially unfair that some indeed are extraordinary, far beyond the range of most humans? If so, and if the state's job is to minimize unfairness, then perhaps it should undertake to minimize these differences as well. If you spend a few seconds thinking about that you will be able to imagine the directions Vonnegut's story (and I presume the movies) go.
There was another movie adaptation of Vonnegut's story in 1995, this one under the same title (see here). I haven't seen it, but I will put it on my list. (I am a bit worried, however, about Sean Astin in the title role: Rudy might be plucky, but does he have the power and beauty that Harrison Bergeron does?)