In this regard, I never really understood how people can "feel" like they "play a role" or can be "immersed" in a world that doesn't react or answer their actions. If, as a GM, I didn't properly answer my player actions, they would be pissed off... For example, when I see people "roleplaying" in, say, Skyrim, pretending that they're resting or hunting to feed their character when the game (without mods) doesn't take those parameters into account at all, it boggles my mind. They claim that, this way, they're more "immersed" in the experience, but, to be honest, if find that absolutely ridiculous, because it doesn't make sense to me, it just seems pointless. The idea of "playing a role for yourself" is indeed very weird to me. Why play a role when there's no audience (or, rather, no other participants) ?
To me, "immersion" has nothing to do with pretending or roleplaying or anything. Just being absorbed in a convincing game world, which thus needs good reactivity and enticing gameplay.
I think it's about imagination (or that may be a good way to look at it) - an extension of that basic ability we have especially as children to engage in fantasy and play. There is no need for an audience or anyone else at all when you have the power of imagination. And some people just like to use it to enhance their cRPG game, their play in it. The game may be displayed on your screen but it is actually taking place inside your head after all.
Whether one likes to control the character as a puppet or to imagine themselves AS the character (either as one you create with a backstory & everything or just a form of self-projection)... these all seem like perfectly fine ways to play an RPG to me.
I do appreciate it when a game takes this second style of role-play into account by providing diverse dialogue options to facilitate character expression and the illusion of choice where mechanical choice cannot be budgeted for. I suppose most people would prefer mechanical reactivity wherever possible, but obviously a video game can only be programmed to do so much. So it is nice when a game is conducive to, and stimulative of, one's imagination through dialogue options and a rich world.
Personally I 'roleplay' in the first way when playing a game like Dark Souls, but prefer to play in the second way when playing a game like Baldur's Gate that provides a reactive enough world to support the creation of (believably imaginable?) characters whose adventures I can experience through the synergy of a computer and my mind. In Dark Souls there doesn't seem to be much point, in Baldur's Gate there definitely is for me.
I think a good indication of the depth of an RPG (in terms of its, you know, RPGness ;-) is how much it supports this second type of roleplay, whether the game is played like that or not... because this also provides an indication of the complexity and cohesion of the gameworld, and the characters who dwell within it.