Marisa (original) researches dark magic and becomes a crazy super-witch. Mima attempts to stop her, but fails. Reimu (original) evidently powers up and kills her, saving Mima in the process.
Original Reimu (who later dies if her lack of on-screen time tells us anything) has an identical-looking daughter, also called Reimu. Meanwhile, Marisa (new) reincarnates somewhere in Europe or America in the past, where her mother is burnt as a witch.
Then, just as Marisa's about to suffer the same fate, evil!Yukari (who can apparently travel through time) intervenes and throws her into Gensokyo.
There, new!Marisa meets new!Reimu, and Mima (who being an immortal ghost has neither aged nor died). Reimu is suspicious, but Mima takes to new!Marisa (presumably because she was hit hard by original Marisa's evil-conversion and death).
However, it appears the evil spirit of the original Marisa is still around in some form, and is pissed that this new Marisa is stealing her stuff.
...I think that's the gist of the story, right? Anyone care to correct me? The whole thing is already a bit convoluted, and it being only half-translated just makes things more difficult for me.