What it suggests is rather scary! If you look at it one way, what this story seems to be saying is that whatever you experience fully, and want to experience, can become real!
The children live in their artificial, telepathy-controlled, holographic world of the nursery. Their thoughts and whims are translated into viewable, sensible images (and maybe something more!). This means that they do not have to do anything more to work for it (such as traveling to the actual African veldt) than think. And that is a kind of absolute power -- the power to have all whims granted without one's own labor -- and it is an old saw that power like that corrupts.
So, the experience of having their wishes granted fully, such as by the holographic nursery, means that the children's experiences are almost all their own. They are able to experience the life-and-death natural struggle on the veldt, rather than the world of family, home, and school around them. They are able to tailor it to their whims, and thus it becomes more compelling and interesting to them than anything or person outside of it. Since the children control their experiences fully, this story seems to be saying, they are able to control the bent of their characters. The experience of having absolute power over their surroundings as made them desire nothing more than that -- absolute power. And this experience of power, denied to every generation of children before them, has made them murderous. They want to remove the people who are going to limit (or cut off) their access to ultimate power over their environment; and those people turn out to be their parents.
There is no indication in the story that Wendy and Peter would have been murderous children without the influence of the automatic nursery. What is being said here is that the experiences the children were allowed to have, when given free rein for their imaginations, warped them to such a degree they would kill their parents. This is powerful claim, for it doesn't take into consideration the inborn character traits of the children; in fact, that is the point. The addictive power of the automatic nursery made their characters subside to such a degree that they would do anything to keep having access to it, including leaving their parents to be eaten by lions. Whatever Wendy and Peter might have been like before their experiences with the automatic nursery has been pushed aside -- the addiction takes precedence.
This would seem to be a cautionary tale (or a grim prediction about the introduction of television, as this was published in 1951) about bad experiences. It is known that, for certain people (and those who are young are certainly included in this) very violent or negative experience can completely change character, and drive the experiencer to commit acts they would not have before. Bradbury is positing, perhaps, that the artificial power that the automatic nursery confers onto its experiencers (the children) will enslave them completely. The analogy to television (and video games, and virtual reality) is uncanny and unsettling.