Omelas is a non-traditional dystopia. Typically a dystopia is portrayed as having a "big brother" type of government that is all-controlling and repressive. About Omelas, it is said that they have no king. Indeed, they have few rules of any kind:
"I do not know the rules and laws of their society, but I suspect that they were singularly few."
Omelas also lacks the traditional organs of a dystopian state:
"As they did without monarchy and slavery, so they also got on without the stock exchange, the advertisement, the secret police, and the bomb."
In short, they didn't have any army or major financial institutions.
"They were not simple folk, you see, though they were happy."
So far, the description of Omelas is one of a Utopia. But knowing what we know, it has a definite dark side. Without explanation, in order to keep their peaceful and prosperous life, they have to keep one child locked up in a cellar. Toward that child they may show no love, to the point that they are not even able to interact with it. That child is fed but otherwise allowed to fester in that cellar, degenerating into madness, until illness claims its life.
This is where the dystopia comes in. It's sort of a play on the "caste system" of dystopia, but unique in that only one individual is made the scapegoat for the town rather than a whole class of people. Though most dystopian stories involve a good deal of conflict between the government and its citizens, because Omelas doesn't appear to have a government, its system remains in effect by mutual consent. Those that don't agree with the system simply leave without trying to change it.
"These people go out into the street, and walk down the street alone. They keep walking, and walk straight out of the city of Omelas, through the beautiful gates. They keep walking across the farmlands of Omelas. Each one goes alone, youth or girl, man or woman."
This, too, is unique to the story. Most dystopian fiction focuses on characters attempting to resist. In this example, people who disagree simply move on.