Defining things is quite simple, really. Just be logical and objective about it.
To me, a ROLE-playing game implies that you can play a role. What is a role? It's a specialized function of your character, just as a police officer is a specialized role in the real world with a specialized function. What defines their functions? Two things: How the character is played and how the world reacts to you. Again, real-world example of a role: A police officer is better with a gun, typically more authoritative and brave than the average citizen, has the right to arrest and investigate people, and the world reacts to him differently, either out of fear or respect or whatever. Without these traits, what seperates a police officer from a citizen? Nothing. Thus, these are vital in defining a role, and the specific functions per role should be unique from character-to-character, obviously.
Skyrim severely lacks the latter part while not being super-strong in the former. The latter part (the world reacting to you) practically doesn't exist in Skyrim. Nobody cares who you are or what you do, the exception being the guards. It's VERY limited.
The former? Characters do play differently, yes, but again, Skyrim seems limited to ~3 playthroughs and ~3 roles, as you can easily make a thief, a mage and a warrior and you'll have explored it all. Any combinations of the three specializations basically feel the same.
In that sense, does Skyrim MEET the definition of an RPG? Yes it does. The issue is to what degree. It's very weak in meeting the definitions. This would basically be as if I called Grand Theft Auto a racing game, or if I called The Legend of Zelda a platformer.
So yeah you can look at the RPG and say it is one, but I think the degree is more important. I mean, one could argue that a game should be classified into whichever category it BEST meets, and I think we can all agree Skyrim definitely meets more qualifications for Action/Adventure than it does for Roleplaying games.
I get where you're coming from. I was going over a lot of the options Guards have in terms of Dialog, and if they had only expanded that to include all citizens of Skyrim, or Most (Maybe a Begger wouldn't know Ebony Armor from mud body paint), the world would have seemed a lot more believable. Well... with one exception, they really need to change the dialog responses for Skills above 30... At least boost it to 75 (Expert)... Or better yet, react to your three highest skills.
There's nothing wrong with an Adventure game though. I personally believe Skyrim is tenfold the RPG that Dark Souls is, and for some reason, that game is lauded for being "Sooper deep and mega rewarding" (How deeps is spamming Ironskin and END upgrades, really?) as an RPG. For me, under those guidelines, Elder Scrolls has always been an Adventure game, on the cusp of a true RPG like Fallout(series). They never truly gave you a third dimension to your character development even at it's best, but at least Daggerfall and Morrowind were ambiguous enough to allow freedom of imaginative interpretation. Oblivion, and in particular Skyrim threw that out the window.