Indoor Cats Indoor cats like to play with dogs, sometimes, unlike what cartoons show. Some cats don’t get along with dogs, though. They like to play with things that dangle and like balls of yarn. Kittens and all indoor cats like attention most of the times, and cats will fight for their territory. Cats, like dogs, enjoy playing fetch when they’re kittens, sometimes. When a cat owner is on vacation, the cat should either stay at a boarding cattery or stay with someone who knows all about cats and are trust worthy.