Playing card? Cluny museum, Paris
Chess came to Europe from the Islamic Empire. People began play chess in Europe toward the end of the Middle Ages, and after paper reached Europe from China, playing cards also began to appear in the later Middle Ages.
We also see more children's toys from this time: whistles and little dishes and dolls. People didn't sit still all the time- they liked to go swimming outside in ponds and rivers, too.
As for spectator sports, the gladiatorial games of the Roman Empire ended with the fall of Rome. In the Christian era, men no longer fought men to the death in the arenas.
But many similar entertainments survived and flourished. In the old amphitheaters, many of which still continued to be used, men continued to fight animals: bears and bulls were the most popular of these, because they were the most dangerous. You can still see bull-fights today in Spain (and in Mexico), and they are still fought in amphitheaters. And people who had been convicted of crimes continued to be executed as entertainment.
In the old circuses, also, horse-racing and chariot-racing continued to be popular for a long time. This was especially true in Constantinople, where the charioteers (the drivers) were divided into teams (the Blues, the Greens, the Whites, and the Reds, though the Blues and the Greens were the most important) and which team you rooted for was tied to your politics and your religion, and often led to violent riots and murders in the circus and in the streets. But on a smaller scale, horse-racing continued in Spain and Italy also, throughout the Early Medieval period. You can still see a medieval horse-race today at the Palio in Siena, which is held every year.
Roland jousting (Chartres Cathedral, France, 1200s AD)
Instead of the old gladiatorial combats, the medieval world introduced the tournament, in which armed and armored knights fought each other for prizes, and for the entertainment of the king and queen and the public. Tournaments were different from the old gladiatorial games in two ways. First, they were not intended to end in death, though men did sometimes get killed anyway. Second, tournaments were fought by rich men, not by slaves and poor men. Still, they presented men fighting each other for entertainment, just as the older gladiatorial games had.
These tournaments were also a lot like the popular Islamic sport of polo, which was invented in Uzbekistan around the time of the Parthians, became common in West Asia around 800 BC, in the time of the Abbasid Empire. It might be the popularity of polo that encouraged the people who organized tournaments to emphasize fighting on horseback, rather than on foot as the gladiators did.