There are many who would argue that despite the nightmarish setting, this game isn't much scarier than a difficult hack and slash. However, I'd argue Bloodborne is actually survival horror. It meets most of the criteria, just in different ways.
Like many horror games, Bloodborne's player is one of the weakest characters in the game, and is trapped in an alien, hostile world. This world doesn't relent or go easy on us, so it's up to us to overcome it. The mechanics might be different, but this game definitely makes you fear for your survival.
What seals the deal for me is the game's clear influence: H.P. Lovecraft. It's not just in setting and creature design either; Bloodborne has that nihilistic tone of his. You discover that (spoilers) your progress through the game has only made Yharnam worse, and has little effect on the elder gods around it.
You not only have to overcome great challenges in this game, but you discover your effort was mostly for nothing. Talk about a grim tale! If you're wondering my thoughts on Bloodborne, it's definitely a Good.