As this thread shows, a lot of people have a lot of different, sometimes conflicting, definitions of what makes a game an RPG. The very meaning of the words, a game where you play a role, makes just about every game an RPG by the most literal definition. Since that's not helpful, we have to go back to the games that were initially called RPGs.
Back in the olden days of tabletop gaming, if you said you played RPGs, no one thought you played wargames or boardgames, they knew just what you meant. Character sheets, dice, rule books, maybe some miniatures, maybe some graph paper. You'd gain experience, you'd improve your character and you'd find better gear so you could fight tougher stuff, find better gear and get ever more powerful until your character died, you quit playing or the campaign ended.
With the rise of console and PC games that mimicked RPGs, in the beginning, there still wasn't a lot of difference among the vast majority of games. Maybe the interface was different, maybe you were solo instead of having a party, but you still had stats, gear and opponents that went up in difficulty. More stats, more gear, bigger opponents, and so on.
Now we're in the age (and have been for awhile) of hybridized RPGs. What this article seems to be saying, and what we're experiencing in the marketplace, is that a whole lot of people really don't care about choosing stats, selecting gear and plotting out character advancement. They just want to immerse themselves in a world with as low a barrier to entry as possible and be presented with some narrative choices, but not worry so much about the rest. You're still playing a role, but it's a very predefined one, and the story path, while branching here and there, tends to lead you right along the same storyline. You can't visit Location C until you've done A and B, or while you can visit many different locations, it doesn't matter which location you visit first and they don't have much impact on the rest of the story, providing more of an illusion of choice.
Just to pick two examples, compare Fallout New Vegas with Mass Effect. Right out of the gate, your character in FNV has very little that defines him or her, except that he was a courier and had something unpleasant happen to him, but beyond that the sky is the limit. On the other hand, Sheppard from ME has an extremely hemmed in story, and while choices can be made during gameplay that will impact the outcome, there are many key elements that simply can't be changed. They're both hybrid RPG-FPS games, but FNV retains almost all of the characteristics of the original definition of RPG, while ME strips out quite a lot in the name of a more streamlined and curated narrative.