Another important aspect of "The Veldt's" antecedent action is that George and Lydia do not know their children and don't seem to know how to go about parenting them. When the story begins, the parents don't immediately ask what is wrong with the children--they ask what's wrong with the nursery and then discuss bringing in a psychologist to handle the situation.
At some point before the story's beginning, the Hadleys decided to let other people and other things (namely the house) raise their children. What I find so interesting about this story is that even though it was written decades ago, it is so timely for today's society, in which parents turn over the raising of their children to technology of all sorts or even resort to having doctors diagnose their children before they (the parents) talk to their children themselves to see what might be wrong--"The Veldt" eerily predicts this type of American culture.
In literary terms, antecedent action is all the things that have happened before the story starts. They are not actually present in the story, but they are relevant because the have set the stage, so to speak. This is called 'backstory" sometimes in TV and such.
In this story, the main antecedent action has to do with the kids and the house. George and Lydia Hadley have gotten themselves this Happylife Home that does everything for them. That is important. The other important thing is that they have been spoiling their kids. They have tried to discipline them now and then but have given up every time.
These things put together set the stage for this story and for the horrible fate that awaits the two of them.