Felt like adding my 2 cents here.

Using modern games to define a genre is a daunting task. As most modern games incorporate elements from multiple genres, making it hard to sort out what's what.

We need to step back into the past and look at distinguishing RPG titles, such as, Final Fantasy and Dragon Quest. The first unique thing about these games is that the player can move about as he/she pleases. This freedom allows the player to go around and explore the game's world and accomplishing this at your own pace, with a timer forcing you to go and beat the stage at a blistering speed. On top of that, you have a life guage meaning you won't die within the first touch of a goomba.

However, these traits can easily found in many non-RPG games, such as, Castlevania 2: Simon's Quest. How do you separate the RPGs from the adventure games? By looking at how the player's character grows.

Growth is an essential element in many games as it prevents them from becoming repetitive and dull. When you beat an RPG game, one has to assume your character is obviously much stronger than when you started the game. However, it is found outside of adventure and RPG games in the form of "power-ups".

Do equipment and items bought in stores and found in dungeons help distinguish the RPG?
No, as many adventure games like Simon's Quest, acquiring enough money does allow one character to buy weapons and armor.

What's left? Battles!
This is where RPGs are unique to other game genres. An RPG's main source of growth come from defeating various enemies and bosses within the game allowing the characters to gain experience and leveling up.

A direct correlation between the enemies defeated and a characters growth is the one distinguishing factor.

There's my 2 cents, be happy to hear from others 2 cents, but don't throw them in my eyes.