Immersion is tricky, because it is an incredibly subjective thing. At the end of the day, what immersion means (I think) is that the "veil" separating you from the game is incredibly thin and transparent. Think of it as wearing glasses: if a game is un-immersive the lenses are dirty and scratched. You can still see whatever is in front of you, but you're constantly aware of the fact that you're wearing glasses. An immersive game is like wearing perfectly pristine glasses: you forget you're wearing glasses at all and can just take in what's in front of you.

An immersive game to me is something that successfully manages to both suspend disbelief and sustain the illusion of a living world, letting you mostly forget that it's a pre-programmed game you're interacting with. I always found something like the STALKER games great for this, with their dynamic A-life AI scheduling really selling the whole living world feeling.