Both excelled at inventing games. Our dearly departed buddy loved to play soccer. He would swat one of his fuzzy balls to you and expect it to be passed back. He invented the game, we did not start it. He also figured out how to pull drawers open by standing on hind legs, hooking the top with front paws, and backing up. Drove the wife crazy.
They do invent games. With or without you they are athletes of the house cat variety.
They’re active and extra observant. That’s how my last Siamese learned to use the toilet and opened doors, and as a kitten she flew like no other cat. Curiosity, you know.
Also, our common cat never talked till the Siamese came and taught him.