This is actually the reason why I posted the last entry, where what was going to be a preface became a rant in of itself. A MMORPG conversation was the larger context for this statement that I've been thinking about: in a CPRG, the story doesn't matter.
Or rather, it's window-dressing, just one component among many. To paraphrase my source, it provides meaning for the decisions you make in the game (and the monsters you whack around). To a certain extent, I'll agree this can be true. I appreciate the slightly unique twist on the usual, "Prophesized heir rises to greatness," inherent in Morrowind, for instance - sure, you're The Guy or Girl, but you're also a heresy and deliberately groomed by the empire to use the prophecy AGAINST its originators - but I could happily play the game without it. The extreme example is the old Bard's Tale game ... in which the story is just an excuse for a smattering of dungeons.
On the other hand, what stands out for me about a great CRPG? Sometimes, if the engine is done really well, a unique element in the setting (more about that later), but most of all, the storyline.
A great example of this is Arcanum: of Steamworks and Magick Obscura. Now, the game is somewhat clunky and incorporates far too many, "Run through this maze, my little rats, and kill things!" sequences to avoid some degree of tedium. But ... the evolution of the storyline is excellent, from when you discover that you're not this famous elf reborn - no, he's still living and kicking himself over his old mistakes - to the end discovery of the villain and his horrifying but ultimately altruistic designs. (The Victorian tech/magic fusion is fantastic here, though the worldbuilding is otherwise fairly unremarkable.)
A second example (serious spoilers ahead) is the new Bard's Tale game, which is a fairly standard rescue-the-princess pastiche ... played from the point of view of a womanizing pragmatist who doesn't really want to Save The World. What makes the game is the final sequence when everything is turned on its head. It's an excellent execution of mood, even if juvenile - but the writers played it for consistency.
The third is Betrayal in Antara, which lost out having a sequel - which it richly deserved - because Return to Krondor, which was its game-engine successor, tanked so badly. Again, Antara starts firmly grounded in the tropes, but builds out from there into a varied, unusual story with racial interplay, characters who are antagonists but doing "the right thing," and ultimately a twist at the end that made me do a triple-take - and cry out for the sequel that was never made.
I recognize I've spent far too much time on computer games over my lifetime, but they have shown me something about storytelling and how to wrap it around an interactive frame. And ultimately, for me, the story does matter.