The most obvious cause of a conflict is the fact that an opponent is trying to reach the same goal as the player or to simply prevent the player from getting there. In a single player game like Dark Souls, clearly every enemy in the game exists with only one purpose: kill your character and stop you from proceeding further into the game.
Multiplayer PvP games are so interesting because the game world is populated by real humans, all with the common goal of winning the game at the expense of the other players. Some games might have a much more abstract opponent-time, for example. A single player racing game in a time trial race, for example, doesn’t feature any opponents (neither human or AI).