Skill based games like particularly chess or any other game that you compete with another person requires you to employ your cognitive ability. It is not mental strength. In my estimation, mental strength has to do more with perseverance in the face of hardship or a challenging situation and not in the context in which it is used. You are able to develop your cognitive skills which includes strategy, during a game of chess. Being able to make a quick and correct decision on the spot is another feature that comes out from skill based games.