The author of the Mortal Kombat universe, Ed Boon, recalled in an interview with reporters how his franchise acquired bloody finishing moves such as fatality and brutality. It turns out that the fighting might not have received them, since at the initial stage of the development of the series, some of the developers opposed such cruelty.
As stated by Mr. Boon, initially only Shang Tsung had something resembling a fatality. Later, his move was cut from the game, but they decided to add something similar for Johnny Cage. As a result, some members of the development team opposed such a brutal element, while others were in favor of adding even more fatalities.
So all the characters of Mortal Kombat got their cool finishing moves, which in the future became the hallmark of the universe.