The fighting game known for digitized actors and finishing moves called Fatalities is Mortal Kombat.
Midway released Mortal Kombat in arcades in 1992, although the question’s commonly cited 1993 milestone refers to its home-console versions. The game used digitized images of actors rather than traditionally drawn sprites, giving its fighters a distinctive visual style. Its finishing moves, called Fatalities, could be performed after defeating an opponent.
The game’s graphic violence generated public controversy and contributed to political pressure for clearer content labeling. Alongside Night Trap, Mortal Kombat became part of the debate that led to the creation of the Entertainment Software Rating Board in the United States in 1994.
Mortal Kombat is often dated to 1993 because that was the year of its major home releases, but its original arcade debut occurred in 1992. Street Fighter II was an influential contemporary fighting game, yet it did not define the Fatality mechanic.