First, some background. In Ray Bradbury's 1950 short story "The Veldt", he predicted a world in which electronics were capable of creating a very convincing reality--not so far off from some of the current video game effects that now exist. The Hadleys live in a Happylife Home, which does most everything for them--it cooks their meals, provides their clothes, regulates the temperature; again, not too far off from what can be done today. The feature that seems to the parents, George and Lydia, to be malfunctioning is the nursery. This is the children's playroom, which is capable of producing scenes that Wendy and Peter direct it to, and has in the past had a lot of different childhood-friendly scenes from various children's books or mythology. Lately the children have been obsessed with Africa, and the display is becoming too realistic and violent for the parents. They not only can see and hear the lions, vultures, and other wildlife, they can feel the heat, and smell odors of death and blood. Though they are concerned, and keep planning to shut down the nursery and even the entire house, they are essentially too lazy to follow through. The house makes it so they do not have to do any work, and the nursery so that they do not have to entertain or even interact much with the children. Instead, they ask the children to not have the African scenes anymore. The children say they will not have the veldt in the nursery any more, but it is obvious to the parents that it is still there.
Your question about how the parents spoil the children is basically that they allow Peter and Wendy to continue to have the nursery. They also allow the children to go to a carnival, eat a lot of junk food, and skip dinner. If the children cry and whine, George and Lydia give in. When the parents finally decide to turn off the nursery, they still give in to the children's plea for "just one more minute". The nursery is not malfunctioning at all--it is doing exactly what the children want, which is to do away with their parents, who are eaten by the all-too-real lions.