I don't think the character has to or doesn't have to feel scared. All I mean is that if the character isn't vulnerable then I as the player am not scared.
Fair enough then.
VTMB is an exception since well... it's an exceptional game, it manages to pull off tons of stuff that's admirable.
But a horror-focused RPG could work in my opinion and still follow your requirements, you just have to be creative.
For example, let's say that stats remain the same, yet some function differently.
Strength would work for objects you can move. There could be a number of scenarios where the MC is running away from a monster only to lay an obstacle in its path. You could always say "why can't my MC fight back if he's so strong?" It's simple to fix that by making your enemies monsters. You can be as strong as any strong man but if you don't know how to fight your strength is pretty much limited, not to mention what you'll be throwing punches at aren't human.
Intelligence would go into your ability to read certain runes in dungeons or devise traps for your enemies (of which are limited as well as the resources to make them.)
Dexterity would obviously go into your sneak skill and perhaps even speed.
I could go on but you get the jist.
The problem is "BioWare" which automatically means stuff like character interaction. Well... again, creativity springs to mind. A horror game doesn't need to be set in some dungeon from start to finish. You could have a hub, a town, multiple towns etc...
In fact, I think having safe places to relax yourself after an exhausting journey in shitmypantsland would make the dread to return to shitmypantsland all the more effective.