Live-A-Live: Square's Lost Gem

[Davy Jones]

unfortunately I haven't seen any other games try anything like it.

Well, there's a clone of it:
http://vgboy.dabomstew.com/other/touhoualive.htm

Meiling's Scenario, first part:
http://www.youtube.com/watch?v=lG4hP30_XyQ

At first, I didn't even realize that it was an RPG Maker 2003 game.