It's easy to be a Touhou fan. All music is "Touhou" genre by definition.
To be serious, the regular genre description is still applied, but since character/stage themes are used as the basis, it imprints the character's/stage's emotions, the track's structure, and possibly more things that I currently can't properly desrcibe. So it can make sense to group, say, all Keiki tracks together, because the emotions that exist in Idolatrize World are preserved in the arrangements.