With a handful of game tokens, mouthful of cheese pizza and earful of arcade sounds, people across the U.S. remember going to Chuck E. Cheese and being mesmerized by the animatronic show that Chuck E.

At a Tallahassee, Fla., Chuck E. Cheese location, a police officer told children: “Chuck E.’s busy right now.” By Victor Mather The scene was a little unexpected: Someone being led away from a ...