Well there are different kinds of playing. There is playing that challenges you, there is playing that's just fun, and there's playing that's challenging and fun. Take a deck of cards, and play some solitaire. Challenging maybe, fun? To me yes. How bout Bop It!? Challenging? Yes, fun? Yes, Bop It! Helps with your reaction timing(reflexes).
Relaxing and doing whatever you want helps reduce stress, and increases your work efficiency after you are done relaxing. And if you decide to play let's say a sport then your blood circulation is increased which helps you focus more on your work once you get back. That's why almost all the people have hobbies which include stuff they like to do.