If I come upon a young child who has a good understanding of written English, I'm going to assume he is a gamer. So many people in my country learn to understand English by playing games.
Statistically, people who game consume less passive entertainment, such as watching TV. The result is that they are more intellectually stimulated and active. There's no question that facing a variety of challenges improves your logic and problem-solving ability.
I also see competetive gaming, taken to a high enough level, a great way to gain insight (not just theory) into psychology, your own and others', that is *not* readily available elsewhere. Applying yourself to poker or go can teach you a lot of the same things than working as an investment banker or a strategic planner, but the latter have multi-year barriers of entry.
Just like games, sports are overwhelmingly played for fun. (Not that there is anything wrong with that.) The fitness you gain is a byproduct. Let's say you spend a hour traveling back and forth to soccer practice, play for 1.5 hours and sit on a bench for 0.5 hours for 3 hours of total time spent. The 1.5 hours of exercise you get is geared towards winning the game, and is often quite sport specific - not maximally effective for general fitness. If you only wanted to be fit, you could exercise at home and the vicinity to eliminate travel time. Fitness-wise, 1 hour/day of focused exercise would exceed the effect of 1.5 hours of soccer. That leaves you two extra hours to work, study, socialize or have fun in another way.