What makes "The Veldt" dystopian?

"The Veldt" tells the story of the Hadley family, who live in a Happylife Home

which had cost them thirty thousand dollars with everything included. This house which clothed and fed and rocked them to sleep and played and sang and was good to them.

The house is integrated with a highly sophisticated technology which looks after every need of the individuals living there: it cooks for them, cleans for them, even brushes their teeth and ties their shoes for them. It comes equipped with a nursery for the children which scans the children's thoughts and creates holographic simulations of reality based on what the children are thinking.

[It's a] wonder of efficiency selling for an unbelievably low price. Every home should have one. Oh, occasionally they frightened you with their realism, they made you jump, gave you a scare. But most of the time they were fun for everyone.

The parents, George and Lydia Hadley, are concerned that their children, Wendy and Peter, are misusing the nursery. The children are obsessed with the place, and spend most of their time there. In the past, the nursery has projected their innocent preoccupations, e.g.,

Wonderland with Alice and the Mock Turtle, or Aladdin and his Magical Lamp, or Jack Pumpkinhead of Oz, or Dr. Doolittle, or the cow jumping over a very real-looking moon.

For the past month, however, the children have thought only of the African savanna, and populated it with eerily realistic lions and vultures. Lydia asks George to come look at the nursery because she hears screaming, and both parents find the place unsettling, even threatening. When the lions approach them, they are genuinely frightened, and run out of the room.
Lydia confesses to George that she feels unsettled by the entire house, these days; its multi-functional brilliance has made her irrelevant:

"I feel like I don’t belong here. The house is wife and mother now, and nurse for the children. Can I compete with an African veldt? Can I give a bath and clean the children as efficiently or quickly as the automatic body wash can? I cannot."

George agrees with her that perhaps they need to take a "vacation" from the house, by switching off the technology and living like ordinary people. They're worried that the children won't be happy, but they're more worried by what the nursery has indicated about their children's state of mind:

The children thought lions, and there were lions. The children thought zebras, and there were zebras. Sun—sun. Giraffes—giraffes. Death and death.

It transpires that about a month ago, when the children became fixated on Africa, George had denied them a trip to New York. The children have been "decidedly cool" with their parents since then, and Lydia wonders how they'll react to having the entire house shut down. George replies,

"They’re unbearable—let’s admit it. They come and go when they like; they treat us as if we were the children in the family. They’re spoiled and we’re spoiled."

He knows that there will be tantrums and tears, but decides that he and Lydia will weather these in the interests of the entire family. The parents have evidently borne their children's disdain for some time, but the macabre atmosphere of the nursery pushes them to try and reassert control. Unfortunately, by abdicating their responsibilities as parents and letting the Happylife Home raise their children, George and Lydia have also forfeited any kind of authority over Peter and Wendy. When George asks Peter what his fascination with Africa is, Peter and Wendy both deny having any interest in Africa, despite what the nursery displays. They go so far as to change the nursery setting to the South American rainforest to "prove" to their parents that Africa is not on their minds. This blatant deception convinces George to bring in a child psychologist to advise on what the family should do. The psychologist, David McClean, is deeply disturbed by the nursery, and advises George and Lydia not only to switch off the house, but to leave the place entirely for at least a month to "reset" the children's thoughts. George asks,

“But won’t the shock be too much for the children, shutting the room up without notice, for good?”
[McClean replies,] “I don’t want them going any deeper into this, that’s all.”

The children are furious at the thought of leaving the nursery for any length of time, and throw such a fit that George, in despair, agrees to let them have "one more minute" of nursery-time before the family leaves on vacation. The children run to the nursery and call for their parents to follow them. When George and Lydia enter the nursery, the lions attack and devour them. The children sit calmly at a picnic table nearby, unfazed by the brutal death they have just inflicted on their parents.
So why is this dystopian? A dystopia is, by definition, "an imaginary place or condition in which everything is as bad as possible." The Hadley family lives in a seemingly idyllic home, where their every need is catered to by perfectly efficient technology. This has had the unintended effect of ennervating the adults, who do not need to take any action to care for their family or themselves, while simultaneously making the children spoiled and aggressive. Used to getting everything they want as soon as they want it, Wendy and Peter are enraged when George denies them a trip to New York—far more angry than children raised in ordinary circumstances might be. They focus that rage into a homicidal fantasy of feeding their parents to lions.
All children have rages, of course, and "feel their parents are always doing things to make them suffer in one way or another." But Wendy and Peter have access to a nursery where they can craft their fantasies into highly-detailed simulations, thereby creating a kind of psychic echo-chamber for their anger. They do not have a sulk, work through it, and move on—they channel their sense of outrage into a graphic revenge-fantasy instead, and replay it over and over until it ceases to be a mere simulation and takes on a life of its own.
Bradbury seems to be saying that using technology to accomplish our ordinary responsibilities is beneficial only to a point, beyond which point it becomes dangerous. If technology becomes sufficiently advanced, it may make human relationships redundant, and if that happens, people are in danger of reverting to a very primitive state. When George first threatens to turn off the nursery, Peter cries,

“I don’t want to do anything but look and listen and smell; what else is there to do?”

A world in which all needs are catered for is a world in which no action is necessary; all that remains is for people to passively exist, indulging their emotions as they arise. There is no need for restraint because there is no limit to resources. People are sapped of willpower, and become venal and vicious. Any attempt to reassert a more normal relationship with the world, in which a person must give as well as take, may be met with violent resistance, because people brought up in a state of hyper-indulgence see that indulgence as necessary to their continued existence.
With these thoughts in mind, you can view "The Veldt" as a spiritual, political, and scientific dystopia. Science and technology continue to make life faster, more efficient, and more convenient with each new breakthrough, with the result that people do not need each other as much as they need the technology that sustains them. This may lead to social breakdown and spiritual crisis, as spouses cease to communicate, children no longer respect their parents, and everyone is "handled and massaged" to the point where their willpower atrophies. But a gift, once given, cannot be rescinded: once technology has become embedded in people's lives, once a benefit has become an "entitlement," it is impossible to undo its effects or to disentangle it from the social fabric. Attempting to do so risks ripping that fabric, and the consequences can be dire.