I can create my own character, and customize and develop that character in any way I see fit. That character grows within the world in any way I see fit. I make choices for my character, and I create the path for my character in any way I see fit.
Essentially, I am playing the role of my character.
Sounds like a "role playing" game to me.
And no - -any- game cannot be an "RPG" by that definition. In CoD, you might be in the "role" of a soldier, but there is no choice, nor development in how your character grows within the world. Thus, not an RPG.
Simply allowing you to choose your role and specialisation does not make a game a good rpg... hell, you can choose your role in many FPS, and even games like League of Legends have skill trees...
How good a game is
as an RPG (not as a sandbox, as an adventure, or anything else, but an RPG) is simply measured by how deep the stat/skill customisation is. And Skyrim is very light on that aspect. You just have a handful of armors and stats that are rough and unbalanced. There is no real customisation, unless you pick some bizarre skill combination it's the same as having a number of set classes, as every sword and board character will inevitably end up the same as all other sword and board characters, same for all 2-h, archers etc. It's still better than the atrocity of FF XII which had no classes with the truest meaning of the phrase (but more than made up with it's combat system and multitude of skills) but the average Korean/Chinese MMORPG is 10x better in the RPG aspects.
Skyrim is an amazing adventure/exploration/sandbox game, but in the RPG department it falls quite short... Tbh, it's barely any deeper in the RPG department than the classic Pokemon games...