I have thought this before.
You're right that even if we were to play Street Fighter we would be role playing
...to an extent I think RPG's try to enhance every aspect so it becomes less of a game
And more of an experience as in that you almost have games inside games
So the title is more broad and not primarily a "Shoot 'Em Up"/"Platform"/"Puzzle" game.
You may do those things in the game itself.
And a sense that "Levels" become more "Quests" or "Missions" or even "Triumphs"
To put a more personal feel to it.
And a sense of growth and learning as mentioned previously.
But I agree, as soon as you play a game with Characters you are role playing
Changing characters in a fighting game just isn't as intense as say playing Zelda
In terms of playing that role.
I guess "Puzzle Games" would be the exception of role playing.