Fuck! Really?!?!? More horror?!?!?!? I'm so fucking happy!!!!!!!!
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I realised you actually asked at one point in what capacity the game features horror. I think you got an answer, but I might as well give dev answer anyway.
There is one character whose story revolves around the idea of ghost hunting. It's played relatively seriously (I.E. You can't fuck the ghosts, they're intended to be legitimately dangerous)
Currently there is only one such event which can be played multiple ways as has been said by others. This particular character will have multiple events around this theme, eventually.
As for supernatural stuff, the game does feature magic powers, however in the game world they're rare enough that it's basically only MC who has one in the current version, so its not exactly supernatural themed at the moment. This theme is likely to become stronger as the main plot is developed, but these things take time.