This interdiction is seen on the infield walls of many ballparks. What does it mean? Well, in baseball, "pepper" is an exercise old-time ballplayers used to play. It involved having the player stand with their back to a wall and having a coach stand about twenty-feet away with a fungo bat and a ball. The coach would then hit the ball as hard as possible towards the player, who would have to field it. Willie Mays used to play "pepper" all of the time and he never got hurt. Of course if all ballplayers were half as good as Willie Mays ...
Anyhow "No Pepper Games" means that you can't play "pepper" anymore. Probably because baseball teams are afraid that someone will get hurt (if not the player, then one of the fans in the stands.)