There are plenty of modern horror games with PS1 graphics, from Chasing Static (which is like Silent Hill but Welsh) to Dread Delusion (which is Daggerfall meets Demon's Souls). Richard Aiken has gone back to the source with this first-person version of the original Resident Evil, complete with pixelated zombies.
Though not complete, in the current beta you can explore the halls of Spencer Mansion with WASD controls and headshot zombies with your mouse like God intended. It's being made in Unity, and is currently so bare bones you'll need to press Alt-F4 to quit, but it's neat that it even exists. As Aiken's itch.io page carefully notes, "This game is made only for fans and was made without any intention to make profit."
If you prefer the more polished HD look of the modern versions, there's also someone out there with a project in the works to remake Resident Evil in Unreal Engine 4, again in first-person, though that one doesn't have a playable build available. Of course, you could go completely in the other direction and play Resident Evil 8 in third-person. You've got a lot of options is what I'm saying.