dtgreene: Except that you can have progression systems without levels or XP.
Also, incremental games (like Cookie Clicker, but that's only the tip of the iceberg) would fit that description, and most of them wouldn't be called RPGs.
Warloch_Ahead: I'm well aware. The point of these names is to poke fun at how seemingly dissimilar games are similar, i.e. Far Cry games after 3 have progression systems and XP level ups, but no one's calling them RPGs.
Similarly, SABEOWS can also refer to any game that has tedious enough combat to simply describe it as standing around until one of you dies, i.e. Elder Scrolls melee.
I tend to define RPGs not in terms of character progression, but rather on the emphasis being on the *character's* abilities, not the player's. The player's role isn't to directly perform the actions, but rather to tell the characters what to do.
In particular, it's possible for there to be a game without a growth system that I would count as an RPG.
There's actual games I classify as RPGs but that do not have XP-based leveling. Most SaGa games, for example. From what I hear, Darklands is like that, and there's also the adventure/RPG hydrids known as the Quest for Glory series (and spiritual successors, like Heroine's Quest).
By the way, I should point out that many of the SaGa games are not linear. The first 3 are, but then the series took a direction that's not like what other JRPGs did, to the point where one could make a case for calling them WRPGs; but they're still different from typical WRPGs because they don't simulate the world to the same extent.
There's some other cases of non-linearity in JRPGs. Metal Saga (no relation to the SaGa series) could be sort of seen as linear, but without the usual barriers, allowing you to skip around. Lennus 2 has a couple parts where you have to collect some seals, but there's not many constraints about the order you collect them in. Even Final Fantasy's orbs (crystals in remakes) aren't much constrained; you have to light Earth first, but the remainder can be lit in any order. There's also games like Final Fantasy 6 and Phantasy Star which are linear up until a certain point, but then become non-linear.
Linear WRPGs also exist. Icewind Dale is an example of one of them. Baldur's Gate 1 and 2 have some non-linearity and sidequests, but the main quest is entirely linear. (While I don't count them as RPGs, the main quests of Oblivion and Skyrim are, I beliveve, linear. Arena's main quest is also linear.)