Not necessarily, but it is the only one that currently springs to mind that is not a full on battle type game, or relies on an element of luck.
It is true that chess is a type of war game but the taking of a piece, i.e. its "destruction", is highly stylised. It is therefore suited to a younger audience as well as an older one.
Chess teaches you to pay constant attention, else you become a victim of short term tactical play. It also teaches long term planning and analysis skills. And finally it improves memory and pattern recognition skills as most players will remember either opening move orders or tactical "motifs" that lead to advantage.
Sorry I can't recommend another game but really, for me at least, nothing else comes close to chess for improving reasoning and overal mental performance.