While many people think of dogs as the pets who play games, you can play games with your cat as well. Cats are not as playful as dogs, but they do like to play games. It is just not the same fetch, rollover type of games you would play with a dog.
First, it is important to remember that kittens are more playful than adult cats. Because of this, if you want to play a lot with your cat, it is important to play with it while it is a kitten. Otherwise, the cat will be confused and not sure why you are trying to play a cat game with it.
Another idea is to raise your cat with a playful dog. The cat will often mimic the dog. I’ve had a cat that never licked in my life, but once I had a dog that was a licker, all of the sudden, the cat started licking too. Animals mimic each other just as humans do.