Characterization

I have much-belatedly begun to read George R. R. Martin's Song of Fire and Ice series.

You know the novelist has succeeded in his craft when the characters take on a life of their own in the mind of the reader, as though they were real people, the reader thinking about how a character might react in a particular situation (not in the book(s), perhaps imagining conversations with the character, certainly imagining what might happen next in the book(s), and so forth.

Is there any equivalent to that, in games, other than in (perhaps) a heavily story-driven game? I can't think of one.

(A few days later)
I thought of an answer at least where strategy games are concerned. If the player, when he isn't playing the game, spends time thinking about strategies, what he can do, what his opponents can do, playing the game in his mind, then that's more or less the equivalent of what I was talking about above.