Marik Bentusi said:
I'm confused.
Whether you care about a Pen & Paper character depends on the same factors as caring for any other type of fictional character. If the storyteller can't convey his story well enough to immerse you, that's a problem with the narrator, not the thing he's talking about.
That's exactly it, though. When we discuss our characters from a game like Skyrim or Mass Effect, that's a tremendous amount of contextual experience instantly available. That character is immediately framed by a universe we care about, and scenarios and NPCs we're familiar with. This context gives us a reason to care about the decisions and behaviours of that character.
With a pen-and-paper character, as Yahtzee says, the possibilities are infinite. Effectively there's no frame of reference and trying to resolve one to contextualise that character is an insurmountable task, for the most part.
YMMV