It’s clear that Charlie’s perspective is warped, mired in fantasy, whereas his son just wants to play with the other kids. And with this first visit to the playground, we realize that Charlie’s grip on reality is tenuous at best.
And once again his long-ago bully, Ralph, is there taunting him from atop a large spiral slide. When they get home and Steve begs to go again tomorrow night, Charlie sets his mind to confronting his fears once and for all, and so agrees.
While much has been made of William Shatner's penchant for over-acting, especially during the latter half of his career, he is quite believably insecure and anguished throughout "The Playground".
It's best not to divulge much more, though I will note that this is one of the darker tales of the series—and of writer Ray Bradbury's oeuvre, for that matter.