Hypothetical - Multiplayer Horror

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Or you could literally make other players untrustworthy. Like in LoZ four sword, all players have one goal, but at the same time, they can compete for resources(And even damage other players.) and there's a final score showing who the better player is.

Of course. But I'm afraid that a competitive gameplay often works against fear, be it competition against the computer or against human players. If you're focussed on competition against others, it puts you in a very "gamey" mindset, especially with things like score involved. Therefore your fears are mostly about the underlying mechanics instead of stemming from atmosphere and immersion. You might fear that someone could steal your resources or try to hamper your progress but that's imo a different kind of fear than the fear of the unknown that horror games try to evoke.