Aaronjw13: "a good game, but not a role-playing game." Usually what people mean by that is that there are few meaningful story decisions made by the player.
That may be one way to define a roleplaying game (ie. a branching story), but I don't agree with that definition.
Wing Commander had a branching story (if you lose a mission, you don't necessarily face game over, but go to another mission/story branch, and might even be able to recover back to the winning branch if you do fine), but I don't consider that as RPG, or even an RPG element in a space combat game. It is just... a branching story, that's all.
Or the "choose your adventure" type of games or interactive thingamalings, where you make decisions on key points of the story, and the story branches on those. Still not a RPG necessarily.
If I understood it right, I mostly agree with
dtgreene definition of a RPG. A story may even be totally optional for a RPG.
Now back to Diablo-clones... they are not called RPGs, but action-RPGs. Meaning, they are hybrids of two main genres: action, and RPG. To me that sounds pretty fitting for such games because they indeed partly depend on player's reflexes and eye-hand coordination (hence, action), but also on how you develop your character and in which ways (hence, roleplaying game).
To be fair, most classic RPGs should actually be called tactical RPGs or such because during combat you can quite often use your own tactical skills to overcome more powerful and advanced enemies. Like the way I killed my first dragon in Baldur's Gate 2, I somehow managed to make it teleport into a spot where it got stuck, and then I could simply kill it bit by bit with ranged weapons (bows and crossbows) and ranged spells. If I had had to fight it on open at that point, I would have surely lost.
Fallout 1-2 had a "branching story" mostly in a way that at the end of the game, you are presented with certain summaries of what happened to different towns and persons, based on what you did during the game (e.g. did you complete certain quests etc.). Yeah it was a nice touch for those game, certainly. E.g. if you did this and this and this, then you get the good/best ending for the Necropolis at the end where the peaceful ghouls run the city and learn to trade with other towns, and live happily ever after in their ghoulish ways.