Not everything needs a cutscene. The game *was* made a decade ago. Back then games didn't have elaborate cutscenes and most games relied on the manual to relay story information. Nature of the beast.
Some things about the story are guessable, but I'll leave a direct manual translation to someone with that ability. From what Marshy said before the forum crash, the manual agrees with the American story, but presents it quite differently.
Nobody could make the game "as it was intended". I mean, who's to say how it was intended? Some things, such as Rush's mouth opening when shooting in R Marine mode and R Jet working like MM4&5 seem obvious and aren't really worth the effort. Protoman's power-up is problematic. It's easy to restore it in Gemini's level, but they obviously intended it to be left out. And that's probably due to the non-linear nature of the game. Were it me, I'd put in in Doc Gemini's level, but ... they didn't. There's a LOT of things that COULD have been in MM3. The basics for Beat were thought of for MM3, as well as a minor enemy that was put in MM5. But, just because those were left out, it doesn't mean it wasn't what Inafune "intended."
I wouldn't mind seeing a hack of some beta elements included in the game, and a certain amount of polish added, I guess. It lacks a lot of polish now that we know of several unused sprites and, of course, the controller 2 tricks being easily accessible. But it isn't quite as extencive to say "it isn't how it was intended to be". I mean, the game *is* complete and fairly balanced. I don't believe the levels themselves would be any different than what we ended up with. I don't think things like Beat, the Mega Buster, or Rush Drill (well, maybe the drill, there's a possibility) were ever programmed into a beta game. There are some programming and graphical issues that, I feel, were left rough because Capcom rushed the game. But, just that alone isn't worth it.