Not all Muslims play Chess, not even a majority.
However, chess was originally a Persian Game called Shatranj and still bares that name in several languages. Just as Canadians pride themselves on hockey and Americans pride themselves on Baseball, Chess has been a timeless reminder of Persian history and culture. Since most Persians are Muslims, people may associate Chess-playing with Islam, even though most of the best chess players today come from Russia and the United States and most Muslims do not play chess.