Ima add a bit more here aside from my review of your demo, cuz why not, this is a topic I'm always eager to talk about.
Well the best thing you can do is look at already successful classic horror games, but not the modern ones, rather the retro ones. Look at the Silent Hill series, SIREN series, Fatal Frame series. Cuz they all have something in common and all horror fans universally loved them if they played them.
When designing a horror game a lot of it comes down to who your protagonist is. Cuz it will make a huge difference in the long run whether your guy is an ex-military, can handle weapons of many kinds and can fight back, or if it's a 10-year old girl who can only run for her life. That will entirely change the dynamic of how your game's systems will play out and you want to make a clear decision on that moving forward.
I assume you prefer the armed protagonist, which is good, cuz I think the "run for your life" protagonist gets boring quick. SH, SIREN and FF all have armed protagonist in some way. Even in Fatal Frame the girl has a camera which she can use to take pictures of the ghosts and defend herself through it, as the ghosts get "killed". So even if it's not a traditional weapon, it still is one.
Another important thing is the setting, ideally you want to create a single vast area which you'll trap the player in by some means. Here's some examples: Haunting Ground - castle, RE - Mansion, Village, SIREN - cursed remote island, Silent Hill - .... Silent Hill (lol). And these games do it because they want the player to really get invested in the place they're in, explore every corner and slowly unravel the mystery, it will make a horror story fun when it starts out very vague, you don't know where you are and how are you gonna get out, and gradually explore and unravel everything. Don't throw the player around from place to place too much, establish a single big area in which you'll situate your story.
And lastly (to not make this post too long), of course you need a very established and feared villain. Though this is a vague term, cuz you don't necessarily need to design the next Pyramid Head, your villain might actually not even be a physical being. In SIREN the villain IS the cursed island, the island's curse is what pulls all the strings, so your villain can even be a bigger thing, like the entire area is the evil-doer. So you can really go wild with this and design whatever villain your story needs. But it should definitely be established in some way, so the player knows what they're fighting or running from. At the same time, you don't want to reveal too much though, as what makes these villains scary is not entirely knowing their intentions or what they are. You want to reveal enough so the player really wants to either fight it or leave, but you also don't want to reveal so much that I exactly know what this is.
Start the game slow and humble, creep the atmosphere into the player's mind, then about 20% in, reveal the villain and then spend the next 60% building up the area you're in, making the player stronger and revealing bits n pieces about the force you're against.
Also a BIG game design tip in general: Make the intro REALLY good and intense. It's important for your horror story to have a strong start, so you can lure the player into your world by showing them one of the most intense parts first. For example make an intro section where you'll actually play someone else, and they get into a terrible situation right of the start, maybe kill them at the end of the intro and THEN transition into our main protagonist. Basically do anything so the intro is decent. Then you can make the entire middle section weaker with highlights here and there, and then finally wrap it up in an epic fashion at the end.
