The kind of fear you're talking about is great, but I rarely get it from games. I treasure the memory of playing an "Aliens" mod for Doom. "Keep it tight, people." "Check those corners... check those corners!" You can't see anything, but you can hear the aliens breathing. Then SHRIEK they're in your face. It got to the point where my heart was going a mile a minute the whole time, and it took me a long time to calm down afterwards so I could sleep.
Unfortunately my success at finding good horror games (and horror movies, for that matter) is so low that it isn't even worth trying anymore -- one good game in ten means paying hundreds of bucks to find a good game, plus the frustration of sitting through so much garbage.
So, yeah, I do like the second kind of horror you're talking about, but I've kind of given up on it.
As for immersion, I agree completely. Few modern games are really immersive. Note to game designers: There's nothing realistic about looking at a bush and not being able to figure out whether you can step over it, or looking at a tree and not knowing whether there's an invisible corridor that will prevent you from ducking behind it. Nobody in World War II died while trying to take cover behind a pile of sandbags that were un-jump-overable for the sole reason that they marked the edge of the battlefield. Level designers need to stop putting visual verisimilitude over everything else and once again start considering the verisimilitude of the whole experience.
One aspect that all immersive games share is that you can almost always predict how objects and terrain will affect your movement. Gosh, just like in real life! That's actually more important to immersion than making the terrain look realistic. If you're examining every rock and bush as a game construct instead of perceiving it as a "real" object, then you're going to see the monster, scary noise, or eerie apparition as just another game construct. You think, "Well, here's a new game object. Looks like a werewolf. Let's figure out how to interact with it. I'll start by walking towards it and seeing what happens. I'll probably get killed, but I might as well be systematic if I want to figure out how it works." That's not an immersive experience :-)
"Hmmm, there's a toddler sitting on the floor of my living room finger-painting with blood."
Immersive game reaction: "What... the... FUCK is a mysterious toddler doing in my house? Whose blood is that!!?"
Non-immersive game experience: "I wonder if I can jump over him?"