What I understood from this is that Seija has the potential to become Amanozako, the goddess who, as mentioned in the doujin, is the origin of tengus and amanojakus (or is, in fact, Amanozako, albeit degraded in some form), so Mamizou devised a plan to keep her from turning.
They manipulated Seija into kidnapping Kosuzu, spread the rumor of "a child being kidnapped by Amanozako", so everyone started to believe it was the case. Since this is Gensokyo, belief molds reality and Seija started to become Amanozako, but she stuck to her pride as Amanojaku and turned back.