I think we are going to have to agree to disagree. Roleplaying can be done in a whole different amount of ways, I could roleplay that my character is the Champion Of Cryodill or Azura's Champion, a Stormcloak Soldier, etc. You don't need stats to tell you how to play the game from an RP state.
This is not something we can agree to disagree to. It is not an opinion-based thing. To call a game an RPG means actually putting in RPG mechanics, of which Skyrim has few. By your definition, every game is role-playing game. If I'm playing Assassin's Creed and I decide that instead of being an Assassin, I want to be a thief even though the world and story never recognize me as such, am I then technically role-playing? Is Assassin's Creed then an RPG? What if I'm playing Grand Theft Auto and decide that, instead of killing people and stealing cars, I'm going to be a normal, law-abiding citizen that drives my own car at a normal, realistic speed and goes to the gym on weekends. By your definition, that would be role-playing and Grand Theft Auto technically would be an RPG.
Yes, you need "stats" to recognize some semblance of what your character is because that's what makes an RPG an RPG and not an action game where you're just pretending a bunch of unsupported nonsense. I don't know how you think the world not reacting to anything you do or ally yourself with is a good thing, I don't know how you can think a complete lack of factions (they're not factions, they're tiny, lackluster quest clusters with absolutely no reputation attached to them or your being a part of any of them... they're even forced on the player as though Bethesda wants you to do them all via the main questline and don't give a crap what kind of character you are or who else you want to attach yourself to) is a good thing either, or how a complete lack of any spell creating options, plot choices (I miss Daggerfall), choice/consequences of any kind (the only thing Skyrim has is questioning whether that perk should go here or there and that's it... not much of an RPG), and limited character customization are good either.