Actually, there is. Not an official one (meaning: not written by ZUN, but then roughly 90% of the series merchandise is not written by ZUN), but:
Touhou Musou Kakyou, of which a single episode has been released.
The character art looks a bit sloppy, but that was intentional. ZUN apparently requested lesser-quality characters since the overall animation was smoother that way. Their original trailer had more detailed designs.
We get lots of Touhou in-jokes and a cool battle scene between Reimu and Patchouli, so that's good. And they hired an English-speaking person to proofread their subtitles, so the translation is much better than you'd expect. Also they somehow got ahold of professional voice actors, so the voices are excellent.
EDIT: TeamFourStar is back up under a different account,
here. No videos up just yet, though.