Okay, ignoring Draco18s' blatant attempt to kill steal from me and take my loot, here's what I think RPG "originally" meant:
(semi serious rambling)
First, we have that RPG means "role-playing game".
From the first part, "role-playing", I associate it with stuff like what psychiatrists make people do in therapy, like, pretend to be somebody else.
I don't just mean like, oh I'm Mario, I'm jumping barrels or something, so I'm role-playing. But more like, actually try to act like that guy would act in a given situation, or try to imagine it. Theatre is similar to this... but there's a written plot. Unless it's improvisational. But then not all actors role-play, some just perform.
Then there's the "game" part. If we have a game, it means we have a goal or something. Maybe a way to keep score. Probably interacting with other players is a factor. Maybe we get gold, or points of some sort, or just some sort of imaginary trophy, or a cool castle, or at least the satisfaction of knowing that we completed our task. We may fail at the task (or we may end up doing achieving something completely different but not less satisfactory). So despite the claims of a lot of people "in the industry", there's some sort of win and lose condition (lose = we die, or we don't manage to do anything worthwhile, win = finish the task, or simply survive, which could be the goal, or simply do anything that somehow advances the plot). If losing is fun, then you win anyway, I guess... the alleged "win condition" was still there, somewhere, implied even, even if you found a more interesting win condition.
Now, number crunching. Why do we have that? Do RPGs need to have numbers? And levels? I say yes and no. Numbers/stats are just an abstraction. To what? Well, simple: we're roleplaying, pretending to be someone else. It's easy to be us: if we're great at math in real life, we're great at math in the game. So stats are a way to create a new personality that isn't us. We suck at math in the game, because we have intelligence minus infinity, or Math Skill = abysmal. Whatever. Most roleplaying geeks aren't great at swinging swords either, so a stat lets us pretend to be Conan.
Otherwise we would win by hitting the game manager with a stick, or he would have to challenge us with real-world examples of mathematical problems. That's also a problem because the real GM may suck at math.
I suppose "fair" players could do that without any stat. They'll just say "well, my character isn't a great musician, so his attempt to charm the peasants with his flute enrages them instead!". But some people just can't be helped, and their choice not to invest in flute-playing skill must be enforced somehow. Still doesn't need "numbers" but at least a description, which can just be enforced by the person running the game.
Now we have computers and game consoles. Can you roleplay in a computer? Well... maybe in a multiplayer game for the benefit of others. It's hard for a computer to know if people are roleplaying or not. But some games have nice rulesets for the "crunching" part and someone thought "well, what if a computer does that part!", so basically computer games are adventure games with the "simulation" part of RPGs. Adventure games have a predefined plot and you solve puzzles, but you don't really decide how events are going to transpire, and anything you do outside of the scope of the adventure has no effect.
We still call them RPGs tho, because they take a part (sometimes an important part) of the original RPGs, which is the rules part. Things that don't depend on gaming skill (reflexes, sword swinging skills with a WiiMote) but on pretending that the you that isn't you on the screen can actually swing a sword without beheading himself.
But other kinds of games also have rules! (Archon has rules). Well, RPGs have rules that are reminiscent of the pen and paper rules. That's the basic difference. So a CRPG is, for example, something based on D&D. Because even if rolling 20 + thac0 minus AC or whatever doesn't make a game "role playing", anymore than "take 5 cards and try to match them in pairs, trios and so on" does. But at least it's the same franchise.
Then there's games that didn't exist in pen & paper. But they feel like those. Or something. So we have a game where you have "attack 10 defense 5" and you "level up", well, people call those RPGs. To some, linear games aren't RPGs, and that's fair, since most people consider railroading a bad form of RPG. But of course you'll never have 100% freedom unless you invent a 100% creative computer/software.
So what IS RPG and what is NOT? Well, the answer is... 3.14. I mean Abraham Lincoln.
EDIT: Note that pen and paper role playing games don't always have a "level progression" mechanic. This is almost mandatory in CRPGs mostly because they're trying to be like mainstream p&p in those regards. But look for example at Spirit of the Century, you pretty much start every character at "maximum level" yet I consider it a role playing game. You can respec a little but that's more like tweaking. (and according to the authors, just change is a type of character growth, even if you don't "increase" somehow).