The thing is, #1 is a separate thing that I can experience in roleplaying games - becoming immersed in the tactical-board-game element of the system and acting based upon optimal game-mechanical choices. That's something I used to do a lot, particularly in 3e and 4e (linked more to my attitude as a gamer at the time than anything specific to those systems, I think).I would have thought that was just #1. Meaning you are observing something and intensely interested in that observation. I know chess and programming are kind of out there examples but I think what you said is what I mean as it applied to roleplaying games.
That viewpoint is distinct from viewing the scene from an in-fiction standpoint while being a dispassionate bystander, which in turn is distinct from viewing the in-fiction scene through the eyes of your own very-much-not-dispassionate character. But they could all be considered a sense of immersion.