Destroying cardboard is fine; your cat is enjoying himself and is doing what comes naturally. Chewing on cardboard is more of a concern. Any sharp edges could cause damage to his gums and it’s hard to be sure that he's not eating the cardboard.
The main risk of swallowing cardboard is that it may get lodged in his guts and cause an intestinal blockage. This can cause vomiting, poor appetite, lethargy, and tummy pain, and is considered a critical emergency. If you are worried that your cat has an intestinal obstruction, or that he has swallowed some cardboard, you should speak to your vet clinic immediately.