I think maybe you and possibly some others are taking it too literally. I don't know of anyone that actively engages in make-believe that they're in the game world when they play any game other than some RPGs (mostly pen and paper). The idea is that you're kind of projecting yourself onto the character, if that's any more clear. It's that there's no barrier.

: It's like pretending I'm John Watson, or Ford Prefect while reading their books.

I don't think so. It's different because you're controlling the character's actions-- maybe not all of their actions, but a lot. In first-person games there's the added element of you effectively looking through their eyes.

: I'm all for immersion in games, even/especially linear narratives like Halo
: has been, but let's not pretend Halo is an RPG. Let's also not pretend that
: "blank slate" translates to default, because the usual blank slate character
: tends to be a grizzled white man in modern games. Maybe that's default
: for you, but there's lenty of people who just can't identify with that because
: they're neither white nor male.

That's getting onto a whole other topic. In the games (except for the legendary ending of Halo 4, for reasons I still don't understand), the Chief has no outward physical characteristics other than being tall, and you only know he's male because of the voice acting and a few instances of "he". Without the stuff provided by Nylund (he's white with brown hair, he was abducted and more or less brainwashed at a young age, he has innate physical differences from regular humans now, etc.), you could peg him as any ethnicity, almost any age, you could fudge his build somewhat, you could make up any background for him, and that's good for immersion, because then none of those things get in your way.