Most games simulate human life in some manner, and thus the interests. Hunting games, where man pits his skill and cunning against prey is but one step away from a real game where he had to catch the prey in order to live. Thus games of toss or tag where dodging and zig-zagging on the run are involved are but an extension of this very real game, and most players recognize that the skills they are learning are doing more than keeping their body fit. In a pinch, catching prey would be easier for athletic games played in the past. Out maneuvering prey may require physical fitness, but man has long relied on his ability to plan to carry him farther during times of duress. Careful planning saw primitive man escaping the flood, with stores of nuts and grain, and wrapped in warm fur against the winter cold. Thus games honing skill in long range planning are highly valued in an increasingly complex world. Thus the popularity of chess.
Chess matches more than any other sport fit one mans mind against another. All other sports, including fencing, engage in team sports to some degree, and most sports are entirely about teamwork. That great chess masters capture the worlds attention and command headlines is due to the relevance of the game to another real game that humans forever find themselves in - beating out a competitor, and above all, beating the competitor by causing him to seal his own fate. Head-on confrontations may be won, but often cause a backlash or smoldering resentment. Beating out a competitor such that his own moves cause him to lose is a deceptive win, and one that often allows the winner to turn his back on the vanquished as they often dont realize the game that was played! Lawyers who seem to have a stumbling presentation but win the case anyway, salesmen who are honest about some of their products weaknesses but walk away with top sales anyway - check mate!