I'd love to know the story behind this scene, assuming there is one.

It's inspired by Touhou - Infinite Spiral videos, but that's pretty much all I could find. It seems that those are unknown to English-speaking fanbase yet.

Daww...They took down that channel. I really dug that music for the opening in the middle there...

There is still chinese translation.
http://www.youtube.com/watch?v=wxSSsapHxu0&playnext=1&list=PLF3983214F61B8A08&feature=results_main

Also 【1000年後に】東方無限螺旋第 search on nicovideo works just fine.