You ever hear of Laplace's Demon? I haven't played it myself and don't know if you'd like it, but Daria thought highly of it:

https://www.youtube.com/watch?v=W2jcJ9TYkwQ

Personally, I think it'd be boring if all scripts of any particular genre were handled a certain way. There should be games where monsters, ghosts, aliens, etc. just plain exist, and there are tons where that's the case, but I think there has to be some unknown factor to make it scary. Otherwise you just accept it as a normal part of the fantasy world of the game. I don't think anybody's freaked out by, say, Starky from Chrono Cross. Being unable to distinguish from reality and hallucination is a pretty terrifying concept, so I think it's fine for a horror game premise. And it's more interesting if there's a backstory to explain why characters can't than to just be like "they're crazy, the end."

If a bajillion works take inspiration from a single source, again, I think all different kinds of approaches keep things fresh. It would be boring if every work taking inspiration from Lovecraft strove solely for faithfulness. Personally, I enjoy a series called The Elder Sister-like One. It's basically a demented romance manga about a boy and a demon girl version of Shub-Niggurath. I'm guessing you would hate it, considering it focuses almost entirely on the relationship between the characters. I'm all about character dynamics and psychoanalysis of characters and so on.

Maybe I've just had back luck, considering I haven't played many, but under-explaining has been a reoccurring problem I've had with the horror games I've played. Keep me guessing through the whole game, fine, but I expect something definitive to come out of the ending at least. But some leave it open to interpretation all the way through, which makes me feel like there wasn't really a plot to begin with, just a bunch of random creepy scenes that you can headcanon in whatever way you want. If it was all in the character's head, at least tell me as much. Don't leave me hanging with "Maybe it all really happened, maybe it didn't."

All that said, I think video games are, generally speaking, a poor medium for storytelling. For most games, the story has to serve the gameplay, which invariably hinders storytelling. The only genre of games (which some would deny are "games" to begin with) with stories that can rival novels and movies is visual novels, in my opinion. And there are some pretty cool horror-themed visual novels.