The reason why cats like to play with chestnut shells may be because they find chestnut shells interesting, or because they can satisfy their predatory instinct while playing. The soft, chewy texture of chestnut shells may be attractive to cats, who may grab onto the shell and gently scratch at it with their paws. In addition, cats may also bite chestnut shells with their mouths and pull hard, which may make them feel a sense of accomplishment.
Sometimes, cats will move chestnut shells to another place to play, just like they move small animals to another place. Same place. This may be because cats find chestnut shells a good "prey" and they like to play in their territory. Overall, cats may enjoy playing with chestnut shells because they find this activity fun and it also satisfies their predatory instincts.