Well, first you insisted that the "role" in role-playing was a character class.
Then you said it was the character, as if in a story.
Then you argued for the character class again.
Then, when I called you on it, you referred back to your post about it referring to the character in the story.
Now, when pressed, you insist that that's not what you meant.
And someplace in there, you brought in first-person shooters (in which you play a collection of guns and bombs), and Myst.
Tell me again, what was the character's name in Myst?
The "role" in "role-playing" is the character, the persona you take on in the game. The name and the personality, their style and way of doing things. You're not an axe with legs, you're not a collection of guns and grenades, you're not a nameless ambulatory camera, nor are you playing a profession or an arbitrary label wrapped around some skills. You're playing a person, like a character in a play or a book.
But the game isn't a pre-written story or a scripted play. You write your own dialogue, make your own choices, and those choices affect what comes next. The future of the game world, the future of the character, the outcome of the adventure are not yet determined, and if you want a "happily ever after", you have to earn it.
That's the "play" part of "role-playing".