So I got Touhou 7.5: Immaterial and Missing Power, but suddenly I've been thrust into a world where 12-year old girls wearing strange outfits and wielding dangerous weapons scream japanese at each other before firing off gratuitous amounts of magical projectiles in all directions. What's going on here? What is the plotline of these games?
You mean it's not clear from the translated summary? ;)
Still, a slightly more coherent description is given here:
Still pretty bizarre, but then, that's practically the definition of anime...
Note that there are further dialogue translations provided in that first link, that will probably prove helpful if you really want to try and understand the details as the story unfolds. Good luck with that. ;)
According to Wikipedia:
The Touhou Project Series is known for their signature Bullet Hell gameplay, the developpers have incorporated this type of gameplay in a fighting game instead of a shoot'm up, by focussing on projectiles