Science Fiction, Tragedy, Horror, Dystopian Fiction
Science Fiction
Some people argue that Bradbury isn't a science fiction writer because his science is all made up. Like "odorophonic" and "mental tape"—those aren't real things based on scientific fact or theory. Bradbury is just making them up so he can talk about how people use new, fictional technology.
But that's precisely the point, folks. That's why we think of him as a science fiction writer in the first place: his stories are about people using new technology. And misusing it, to be sure.
Tragedy
We consider this a tragedy because it ends, well, tragically for George and Lydia Hadley. (To be fair, if you're a lion, it's a happy ending indeed.) Plus, these parents are killed by their tragic flaw: plain old bad parenting.
Frankly, it's hard to imagine what a happy ending would even be here: if George gives in to his kids, he has failed as a father. If he opposes his kids, they're going to kill him. And that's a classic tragic choice: failure or death.
Horror
Like most stories where children use fake lions to kill their parents, there's something a little horrifying about "The Veldt." It could easily be an episode of Tales from the Crypt. (Though they usually use ventriloquist's dummies—not virtual felines.)
Dystopian Literature
Dystopian literature is all about terrible societies of the future. Think Panem from The Hunger Games. But all we ever see in "The Veldt" is one house and one family (plus their shrink). So how in the world could this be considered dystopian? There's no society.
We're calling it dystopian because this very same story could be taking place just about anywhere. Parents and kids could be struggling over control of nurseries (and other gadgets) all over the world. As David McClean notes, "too many others" (203) are having the same experience of using too many gadgets. Okay okay, so maybe virtual reality lions aren't eating parents in every house. But just about everyone is clocking too many hours on their electronic doohickeys, and that's what makes this story a rather universal, rather terrible vision of the future.