My views on horror are a bit more broad. Survival Horror doesn't always scare me. RE1 isn't a frighting game to me but man do I get a kick out of it, out of the whole experience, and I do consider it a horror title. But that's not saying much since I still apply the term to other titles. I consider DMC1 and Bloodborne horror games; the fact that there is action is irrelevant because I found myself actually scared when I play those games, not with DMC1 anymore, but the first time, in a dark room and with headphones, yeah, I found it scary. Rule of Rose, another favorite of mine in the genre, isn't scary at all, but I qualify it as a horror for it's unsettling nature.
Like I said before, horror is a very broad genre, it's not just fear for your life that can make a quote on quote horror experience.
Games like RE4, for example, aren't scary but I consider it horror because it delivers a tense experience. The first time I played it I was actually shaking and my heart was pounding trying to survive when I first got into the village. To actually trigger fight or flight instinct in a game is hard to do so props to it. Unfortunately once you've experienced it in one game it's not likely to happen again. Games like Bloodborne, The Evil Within, and Alien Isolation do the intense experience very well.
Silent Hill starts out telling you exactly the kind of horror it is. Fear of the blood leads to fear of the flesh. It's the type of horror we call psychological, because it studies human fears that originate in the psyche and not in something more primitive, like the fear of the dark or predatory creatures. These are fears of the dreaded things of the mind and the flesh. Fear of the rotted, a hell of steel, rust and blood, of tortured creatures.
Lovecraftian horror doesn't seem to translate well in to video games. The idea of cosmic horror is to learn of the absolutely minuscule scale and impact that is man and humanity, that there is something more powerful and infinitely older living in the darkness, something hostile, and no amount of technology or knowledge can make man equal to the oldest forces of the universe. Fear of the cosmic, of the immensity of the universe, and the Lovecraftian lore form this genre and ironically the closest a game's gotten to represent that is Bloodborne, thought there are still horror games based on the Cthulhu Mythos, though I hear not many get it right. I'm not big on this one and I don't seek it out but after playing Bloodborne I have more interest in it.
Rule of Rose is not about what's frighting, it's about what's twisted. Not all horror games focus on what can frighten a person but rather focus on twisted ideas, behavior, or concepts, sometimes human and sometimes not. This is still horror, though not necessarily the scariest of horrors. It won't keep you up at night nor will you be scared to be alone after, but it can leave lasting impact because it can be as powerful as a drama.
Biological horror is big in Japan. It's the idea that the body will degenerate or advancement will create horrors of the body. Resident Evil and Parasite Eve are good examples but it's more about disease, mutation or the decay of the body through nature or man's actions. Outlast might be a better example, from what I've seen.
Of course there also atmospheric horror, which depending on the title might be the opposite of survival horror since it doesn't mean you can actually die. I've heard they're out there but I've never played them, games that focus on creating a frighting experience through ambiance and atmosphere but you don't actually die, you just move through it, like a haunted house. P.T. might've qualified if there wasn't that one instance where Lisa can kill you, though I've heard you don't actually die in SH Shattered Memories you don't actually get killed by the creatures, they just take you back to the beginning of the level, since they are the representations of the daughter's psyche and she doesn't want to hurt the father. Those aside, though, I've only played a few games where the atmospheric horror is the focus; plenty of them have atmosphere but few make it the focus, like Daylight, but I know they're out there.
These are the ones I personally go out of my way to play but of course, like film, there are plenty of other sub genres, or themes in horror but games tend to have a mix of more than one. There's the creature games where the creatures a where the horor comes from be it zombie/vampire/demons/aliens, the serial killer, paranormal/supernatural/occult, Japanese themed ala Ring or Ju-on, ghosts/spirits, Gothic, teen slasher just became a thing, and others I can't even think of.
Like I said, it's a very broad genre.