It's exactly what I thought after reading the novel, however what you say in the last paragraph is not entirely true. If you consider "free will" in BNW the same as it's in the real world, Alphas and Betas do have it, and the overwhelming majority of them choose to exercise hedonism (the minority being the people sent to Falkland islands). As for meaning, everyone in the world is doing their job, and everyone is necessary for the society to exist, even the Epsilons, as shown in the experiment set by the government where they took a group of Alphas and told them to build a society (you remember how it went, don't you?).

The dystopia factor is present in the fact that "free will" in Alphas and Betas is the only thing that's left from the "social" in the "biosocial" human being that we know, whereas Gammas, Deltas and Epsilons don't even have that. Humanity is reduced to the level of animals. They do their job for the survival of society, fulfill their biological necessities (the "procreation" part is the most described one in the novel) and then take soma to destroy any thoughts that can make them human.

Don't know about you, but I don't want to be an animal, neither do most people, and that's why it's considered a dystopia by the majority.

It was mentioned in the story that Gammas, Deltas and Epsilons also get soma after their work shift. However, the theory about BNW being an actual dystopia for the lower classes could potentially be correct if we ever got an insight on that.