There are times when I start thinking about strange possibilities and different experiences of existence, such as whether people with different eye colors see the world exactly the same way. Really, if blue eyed people experienced colors one way and brown eyed people experienced them another way, we would really have no way of knowing, because everything would look normal to everyone. That's a rather childish example, but when I start feeling existential I sometimes wonder if we are all part of someone's imagination or if we are some tiny part of an unimaginably bigger world. The religious implications here are pretty obvious, but Shadow Play has nothing to do with them.
The idea that we are all just figments of someone's (or something's?) imagination is not a new proposal, of course, but Serling has taken the premise and turned it into a pretty entertaining half hour story. Dreams and their meanings is an almost endlessly fascinating subject, and has been explored extensively in the annals of psychology, as well as in film, television, and literature. Wes Craven blurred the lines between reality and nightmare in his Nightmare on Elm Street films, and long before that, Serling explored the causes and effects of recurring nightmares more than once here on the outskirts of the Twilight Zone.
It doesn't seem that the show is really seeking any answers, but is instead just presenting a situation in which a man is having recurring nightmares in which he has been sentenced to death, and is basically trying to convince the people around him to help themselves by helping him.
It is a brilliantly ironclad dilemma he is in. Imagine being on death row and trying to convince the guards and police around you that if they go through with your execution, they will all disappear. "You're all in my imagination! If you execute me you'll cease to exist!" The feeling of helplessness that he must be suffering is unimaginable! Granted, I've had dreams where I sank like a rock to the bottom of the ocean or fell off a building or something, and I always wake up at the point of death, and while it's scary, it's also an enormous relief when I wake up and realize I'm safe in my bed. Still, the nightly anticipation of electrocution's gotta make it hard to get to sleep at night.
Although personally, rather than trying to convince the guards to cancel my execution, I would just stick my arm through the bars of my cell and say - "Come on, pinch me! See what happens!"