Patient Gamers

Signalis is fantastic, it blends the careful resource/inventory management of classic RE with the somber psychological storytelling of Silent Hill (specifically inspired by SH 1-3).

The basic premise is that you're an android named Elster searching for your lost human co-pilot after crashing your ship. The environments range from industrial machinery, to hellish twisting labyrinths, to dense urban corridors. The game is surreal, has an incredible soundtrack, and tells an emotional non-linear story. Highly recommend it.

Don't Look Outside.

It learns more in an RPG direction, but the story is fun and the pixel art is phenominal.

Huh, nobody else recommended Darkwood..

I'd say, give Darkwood a try

Soma

I'm guessing you wouldn't like Alien: Isolation because it's basically all hiding and strategically trying to outwit the alien... while hiding. But it's fucking terrifying and very well-written.

I really enjoyed SOMA during the past winter.

RE7 and 8 were both awesome! Personally I enjoyed 8 a bit more than 7 but 7 was the scarier game by far.

The RE remakes from the past few years are pretty amazing especially if you enjoyed the originals. I just finished RE4 Remake and it's probably the best action horror I have ever played.

The Dead Space remake is also incredible and I highly recommend it.

Some indie titles like Mouthwashing, and Security Booth are creepy, quick, and fun.

Most of these all go on sale every few weeks as well.

Sorry We‘re Closed, Crow Country, and Signalis (was already mentioned but is really really good). The last two have tank controls but are not nearly as clunky or difficult as RE1/2 because of that.

Dead space and dead space 2

So to answer your question, I'm afraid resident evil has cornered the market. I think the evil within might be a close second.

However

Amnesia: The dark descent is the granddaddy of basically every indie horror game you see. Also, I believe, the best one.

I see you said you prefer combat, but if you ever get curious, take heed of the message before the game starts "don't try to win, do your best to immerse yourself in the world" because if you do, you'll be taken for a psychological terror-ride.

Seconding other's comments for: Signalis and Soma

Some unorthodox / overlooked suggestions:

• Project Zomboid (PC).
  • Imagine the Sims 1, but it's during a zombie apocalypse with a GTA sized massive map. The situation is so dire that the game outright tells when you start that your character dies, and the actual gameplay is just you finding out how your character died.
  • The survival: is needing to move to scavenge for resources and trying to build a safe place to sleep.
  • The horror: is trying to escape the literal hordes of zombies.
  • Sidenote: This is a great grindy multiplayer game.

• Metroid Fusion (GBA).
  • It's a platforming game, but it's legitimately terrifying.
  • The survival: revolves being trapped on a space station going around fighting and fleeing difficult enemies
  • The horror: revolves around the antagonist: [redacted for story spoiler reasons]
  • Sidenote: This is a great game to show people who haven't yet realized that you can make horror without being an FPS.

• Frostpunk (PC).
  • It's a city-builder game with survival resource management gameplay and with non-lovecraftian cosmic horror themes.
  • The survival: You are the last city on Earth. If you run out of resources: you die. There isn't enough resources to save everyone and you have to make hard decisions. If the people lose hope from your decisions: you die.
  • The horror: The world's climate dropped another 3 degrees today. There are 100 of us left. Only 5 people from yesterday's expedition made it back with food. We need to send 20 survivors out to look for scrap metal to repair the heating system or everyone will freeze. We need to put our children to work in the coal mine, it doesn't matter how many die, if they don't mine, we all die. The next day: things get worse. The day after: things get worse. etc... Will you survive?
  • Sidenote: This has one of the best soundtracks in all of gaming. I'd put it up there with Halo, Skyrim, Homeworld.

Outlast 2013 has no combat but it's horrific all right. I enjoyed discovering the scenario progressively although it probably has some frustratingly dated mechanics (why closing doors sound so fucking loud damnit?!).
There are two more recent Outlast games I have not yet played.

Signalis. I can't recommend it enough.

Signalis.

I would say Project Zomboid, but I think they've been working on that for more than a decade.

Vintage Story definitely has good survival elements, and shivers are straight horror, so Vintage Story?

Cronos: The New Dawn, came out last year kinda flew under the radar, it's pretty scary, has interesting lore, the ending didn't quite please me but overall I would recommend it.

Has a RE vibe to it, limited inventory, lore through notes, and all that good stuff

Does Rain World qualify?

Lost in Vivo is great. It's all about claustrophobia and psychological horror. Plenty of secrets too!

Of games that aren't pure survival horrors (as in, they aren't shooters): NO-SKIN, Infra Arcana and House of Necrosis.

NO-SKIN is a very weird, moody turn-based roguelite focused on resource management and figuring out secret interactions. It leans heavily into psychological horror side of genre.

Infra Arcana is a mix of survival horror and traditional roguelike. It's lovecraftian horror with weird cults and things from distant stars and all that vibe. Unlike everything else I recommended this game is BRUTAL!

House of Necrosis is a roguelike that takes 'survival horror' more literally: aesthetically, it's pretty much just Resident Evil. Zombies, labs, evil plants, Jill... it's much easier than IA too.

It's not exactly old (it came out this year) but you could give the new remake of Fatal Frame 2 a try. You could play the originals but they are very similar controls to the old Resident Evil games. It has combat where you go into first person and have to photograph "shoot" the ghost/wraiths.

https://store.steampowered.com/app/3920610/FATAL_FRAME_II_Crimson_Butterfly_REMAKE/

Flesh Made Fear, Subversive Memories, and Signalis were good send-ups of the early RE games you might want to check out, though they are third person games

My Friendly Neighborhood is really good

@Apeman42 While it doesn't have the combat of RE, Alien: Isolation is a good survival horror game.