Rock, Paper, and Scissors each have their own strengths and vulnerabilities. Rock is strong but gets covered. Paper is flexible but gets cut. Scissors can cut but gets crushed. None of them wins against everything, and none of them loses against everything. The relationship between them is the whole lesson.
The Rock Paper Scissors Story uses this structure to introduce children to nontransitive relationships — the idea that A beats B, B beats C, but that doesn't mean A beats C. It's an unusual concept. Most of the relationships children are taught at that age are linear: bigger is stronger, more is better, first is best. The RPS relationship is circular, which means everyone gets a turn at winning and a turn at losing depending on who they're matched against.
This is a reasonably sophisticated concept for a children's book, and the story handles it by grounding it in the game itself rather than abstracting it. The characters are the gestures. Their interactions are the outcomes. The fairness comes from the structure.
The book is suitable for early readers and for reading aloud. The illustrations follow the three characters through a day of competitions and agreements. No single character wins everything, which is the point.