I guess your right. BioShock is just one of those games where it should fall under one category, when it falls under another.Well, I guess that depends on what you define as horror. Some people call "The Path" a horror game. Except that it isn't scary, it's just boring and convoluted.
Bioshock isn't exactly horror. The same way the haunted mansion at Disneyland isn't exactly scary. I would call it suspense rather than horror. But in game terms it's treated as an FPS with heavy story element.