I'm gonna call it "Parable Horror" and hope that it sticks. Or maybe "Alle-gore-y"? Wait. Let's call it "Scarable." That's way better. Are we all cool with "Scarable"? I feel like I shouldn't be the only person in charge of naming a new genre... but I also feel like I just hit it out of the park.
I'll give you some scarable examples. SPOILERS AHEAD.
The surface story of It Follows is that an invisible sex demon is sluggishly stalking teenagers like a barbiturated Zodiac killer. If you have sex with someone, you'll pass the burden onto them until they die (at which point you're back on the chopping block). And while there's a lot to love about the Carpenter/Raimi-esque way the movie is shot, the fear comes from the plodding inevitability of death. That one day we're all going to die. After one of our main characters has sex with the other to save her from the demon, the movie ends with the two walking hand in hand with the knowledge that, someday, it will come for them.
Just two young adults in matching outfits walking down an aisle together -- because the bond they share is literally the same as marriage. They are united for the rest of their lives, and when one of them dies the other will soon after. And when you realize this, the ending becomes strangely more positive. These two teens go from fearing the certainty of death to finding each other through it. And sex, which began as the hand-wringing villain, is now the hero of the movie. It's like The Grinch, but with a way different organ growing three sizes larger.