Chess from India
The big new game of the Islamic Empire was chess. The Arabs learned to play chess from the Sassanians when they conquered them, and probably the Sassanians learned chess from people in India. Indian people themselves seem to have learned at least some version of chess from people in China.
Backgammon and checkers
People also kept right on playing the older games of backgammon and checkers, which go back to the Bronze Age. Chess helped to replace the gambling games with dice like backgammon which had always been very popular. Islam forbade any kind of gambling.
Playing cards from China
Even so, around 900 AD people in Iran began playing gambling games with playing cards. Playing cards came to Iran along the Silk Road from China, and soon spread west from Iran, reaching Fatimid Egypt around 1000 AD.
Bear-baiting, cock-fighting, and wrestling
Roman-style violent spectator sports persisted into the Islamic period, especially bear-baiting, which remains popular in Pakistan today. Cock-fighting was also popular. But the Muslims did not fight the gladiatorial games of the Romans, where people were killed. In the Ottoman Empire, the Central Asian sport of wrestling was more popular.
People in the Islamic Empire also really liked archery contests. Omar, the second Umayyad Caliph (634-644 AD), apparently told men to, “teach your sons the arts of swimming, sharp shooting, and horse back riding.” Falconry was common as part of hunting, among both rich and poor people.
Polo on horses
Birth of the Chess Queen : A History, by Marilyn Yalom (2004). How the game of chess changed from West Asia to Europe.
Arab Falconry: History of a Way of Life, by Roger Upton (2002).
Al-Mansur’s Book on Hunting, by Sir Terence Clark and Muawiya Derhalli