It's all just an argument over a word. When you're immersed in a game, you're hooked to something in it, whether it's immersed in a game's world, story, characters, gameplay, etc. If you feel like you're "really there," then you're immersed. If a character you like dies and you actually care, you're immersed. If you're playing a game, and notice that the last time you looked at a clock was about five hours ago when you first started playing, then you're immersed.
Immersion is an important part of a game for many people. A game can be polished and playable, but if it seems ho-hum or you've played it before, then you're not immersed, and you can care less. But if you've been playing for god knows how many hours, have laughed at many jokes, or follow the storyline, then you're immersed, and allows for a better experience. In this regard, I think most people have experienced it at one point or another, and it equaled a better experience for them.