What is she good at, what is she lacking in?
This is tied to stats, skills, perks, talents and whatever. It is the mechanics that define what my character can do and what she can't do, it defines her abilities as a human being as well as her shortcomings.
What are her morals?
Her morals will be defined by the choices she makes when forced to make a decision based on ethics, morals, ideology. It is about what choice she will make in a quest or an event. Two people are arguing about something, who's side will she take? A homeless kid stole a watch to sell so it could buy some food, what will you do about it?
What is her personality?
This is heavily tied to the dialogue system, what choices does the game offer me when engaging with another character? Can I be a hardass? Can I be sarcastic? Can I be flirtatious? Can I lie? Can I joke?
What are her aspirations?
Basically, will the game allow me to live up to the aspirations that fit the character? What if the character wants power? Can I get that? Will the games story reflect that? If I want something more personal like a relationship or a family will the game allow me to achieve this in some way?
If a game allows me to define my character really well then that speaks volumes about the rest of the game itself. A game that allows me to define her morals will offer me mulitple quest solutions. A game that allows me to define her personality will have a good branching dialogue system. A game that allows me to define her strengths and weaknesses will have a good stat/skill system that is more than just about whether I kill stuff with a yellow, green or purple stick. A game that allow me to define her aspirations will have story elements that offer me choices in how I want to steer my character and I won't feel forced to continue the story-line because a reason that don't fit my character has been imposed on me.
That's what an RPG is to me. It allows me to 'role-play'. To define my character.
Whatever game fits this bill is an RPG to me and a game that allows me to define my character really 'really' damn well is a fucking great RPG. Which is why I think The Sims is an RPG series. It allows me to define all of these things in tons of different ways.
But, and this is a big butt, the most important question comes after all of these definitions; Is the game focused around these or are they just a side-thing?
That's what defines a good RPG to me. But even bad RPG's can have these qualities and still be RPG's, it simply means they ain't good.
Now, as to Fallout 4, it does not allow me to define my skillset really, only choices I get to make is whether or not I can hack, lock and craft stuff. Big whoop. It does not allow me to define my morals for the vast majority of the time apart from the main quest when it splits. Not enough. It does allow me to define my personality, it just does a really damn shitty job of it. And it does allow me to define my aspirations as it has a branching narrative. So it completely fails on 2, it's bad at 1 and it fits 1.
It's not an RPG to me. An RPG to me needs to fit 3 out of these 4 definitions to even be considered one.