The Peter Pan archetype is obviously used and it's made obvious by the use of the children's names Peter and Wendy. In fact, the use of the term "nursery" recalls the nursery in the J.M. Barrie work. And the magical world created in the magical screen recalls Neverland.
The Peter Pan archetype focuses on the child's refusal to grow up and the vilifying of adults.
These ideas are clearly present in "The Veldt" as Peter and Wendy rebel against their parents, who want to take away their magical world that occurs within the nursery. In fact, the parents desire to take out the nursery suggests a desire to make them grow up and spend time in the adult world.
So, with the children's names, the magical world and the "nursery," Bradbury is obviously create a connection with the archetypes created in Peter Pan.