I think that this story points to the need for discipline and limits -- the fact that these things are needed in order for children to maintain their dignity as human beings.
When parents let their kids do pretty much whatever they want, they are taking the kids' dignity. They are sending the message that what the kids do and what they become is not important. In this story, the parents neglect to really try to discipline their kids. In doing so, they take away the kids' dignity and the kids, in turn, take that of the parents.
I think that the Bradbury construct of technology is one where individuals tend to remove the dignity of others as they substitute “things” for people. Consider the children as an example of this. The boy and the girl grow so dependent on their technological construct that they cannot stand the very idea that their parents would seek to enforce some level of control and limitations on their enjoyment of the room. The children become so dependent on the room and the need for technology in their lives that they actively conspire to eliminate the single threat to it: Their parents. In their love for technology, the children sacrifice the dignity of their parents and are easily ready for them to be sacrificed at technology’s altar. Had there been dignity of the parents seen in the eyes of the children then I think that they would have reconsidered their actions. When the parents’ dignity was removed from the children’s emotional sight, it became easier to eliminate them. Technology and the love for it is something that removes the dignity of people quite quickly, making it easier to dehumanize and eliminate them from one’s emotional frame of reference.