The closest Chinese equivalent to the Roman public spectacles is probably the Hundred Events (百戏) of the Han dynasty (206 BC–220 AD). The Hundred Events included a variety of entertainments. There were dances, wrestling, singing, boxing (which was considered distinct from wrestling), feasting, archery, "tripod lifting", stone turning, fencing, and others.

Wrestling in China was considered a foreign sport, likely from the steppes, but was popular among the elites and the ordinary Chinese. In armed contests, there were competitions for each of the Five Weapons, including spears, swords, staffs, halberds, and long swords.

The Hundred Events were open to the public, attracting people from all over the Han empire. The Chinese emperor Han Wudi hosted a wrestling contest in 112 BC and 109 BC, which were both very popular among the masses. The emperor held the Hundred Events to publicly demonstrate the power and wealth of his empire. Furthermore, the events were used to impress foreign envoys. Martial contests like wrestling were spectacles that showed the envoys the military prowess of the Han dynasty.

Source:

Lorge, Peter Allan. Chinese Martial Arts: From Antiquity to the Twenty-first Century. New York, NY: Cambridge University Press, 2012.

Public executions! Everybody loves a public execution! Have you heard of "death by a thousand cuts?" That was an actual torture/execution technique in ancient China. Essentially, the person to be executed would have varying parts of his body cut off, one piece at a time, in a public place. First it might be his fingers, then his arms, then his feet, half his leg, the other half... And it would be quite the spectacle, watching as the victim screamed his/her head off.

If watching humans die terribly doesn't fit your taste, perhaps you'd prefer cricket fighting! If you've seen a cockfight, its basically the same thing, except with... male crickets! Dating back to at least the Tang dynasty, two crickets would be placed near each other and instigated to fight each other. These crickets would often have been bred specifically for combat, and peasants would search for crickets that were big and strong to supplement their income. They would sell the crickets to specialized handlers that would raise them for combat. Cricket fighting still continues to this day, although it was also banned during the Cultural Revolution.

Source: Werner, Ancient Tales of China

I'm not sure if this is what you were looking for, but something similar to Roman gladiatorial combat in ancient China was the Leitai. It was an elevated platform on which two competitors fought. You would lose if you submitted, were incapacitated, or were forced off the platform.

Medieval tournaments did not perform a similar function to Roman games. They were martial exercises which later became a rarified form of entertainment for the social and martial elite. They were not designed to win the love of the masses, but instead the love of an exclusive social group.