Video game bad guys generally are all part of the same organization. So when you reach the final bad guy he is usually the one who has been organizing all the other bad guys. So that would make him their boss.
So in games where you are fighting an organization or maybe an army, the final boss is literally “the boss” of all your enemies. That particular plot is pretty common so it just became common to call the bigger bad guys “bosses”.
Early arcade games, particularly Contra, Double Dragon and Kung Fu literally called them “the boss” in the game and in the instruction manual. After that it stuck.