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 man's 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.