The term "role-playing game" has become somewhat nebulous and unhelpful these days when it comes to categorizing video games, in large part because so many games have started implementing RPG elements in their gameplay designs, causing the line between "RPG" and "not-RPG" to blur. Sometimes the distinction is easy to make, if the RPG elements are obviously secondary to some greater gameplay emphasis, but the advent and popularity of hybrid games (like the Mass Effect series, for instance, which are equal parts RPG and action-shooter) have raised serious questions about how we should classify RPGs, since nearly every RPG these days now falls on a wide spectrum based on "how much an RPG" it actually is. When thinking of what games I'd put in a "Top 10 Favorite RPGs" list, for instance, I struggle with deciding whether certain games should even be on the list; for example, is Deus Ex actually an RPG? What about Dark Souls? In both cases, my gut says "no," but you could make an argument for both games, based on how you actually define what constitutes a role-playing game.
A key issue with this debate is that different people have different definitions; for some, the simple presence of a leveling system makes any game an RPG, while others insist that it's more about choice and consequences, while still more people would say that it's about being able to make a character (or an entire party) and explore a large open world, playing the game however you want. In truth, there are a lot of specific mechanisms and general concepts that go into making an RPG, but it's probably not appropriate to draw a hard line in the sand and declare that "if a game doesn't have have these specific elements, then it's not an RPG." As the folks at Extra Credits have pointed out, mechanics don't define genres; why we play them, or what we're looking to get out of them, does. And as the classic Potter Stewart quote goes, "[I can't define it], but I know it when I see it." Which is to say, there's an inherently subjective logic about how we perceive and classify these games, and it's not always easy to put into words. But I'm going to try.