I'll give you a few possible examples of potentially lethal combat sports practiced in other cultures, buy I will refrain from offering an opinion on how similar they were to Roman gladiatorial games, since it depends on which aspects of those games you consider to be important.

2nd millennium BCE Egypt had some sort of combat sport with weapons that was based on sword fighting, but practiced with sticks. Unfortunately, very little is known about the rules, conventions, or spectator appeal of this activity, but it was important enough to have been depicted on tombs at Amarna. link

Ancient Greece had numerous games, most famously the Olympics, which included numerous combat sports. These included the infamous pankration, in which contestants were sometimes killed.

Elizabethan England had its prize fights, public spectacles in which fencing masters were tested for admission to the fencing masters' guild. These were very popular, and by some accounts, quite bloody affairs, although the purpose was to test the applicants' skills, not to harm or kill them. In Restoration England, the prize fights evolved into more of a public entertainment spectacle with professional fighters fighting each other with weapons purely for show. Death was not the desired outcome, but the events were quite bloody, and fatal injuries happened from time to time.

Bare knuckle prize fighting supplanted sword prize fighting in the 18th Century, which gave rise to the modern sport of boxing (which in turn informed professional wrestling and MMA), but the swordplay tradition lived on with singlestick, a rustic "game" played at country fairs in which the objective was to split open the opponent's head with a stick. Drawing a bead of blood an inch long was the purported objective of the game, but occasionally participants would get beaned hard enough that they would die from the injury.