In the names of cartoon movies 桜花抄, 百鬼夜行抄, what's the special meaning of 抄? Is it a kind of synonym of 物語?
The literal meaning of 抄 is “excerpt,” and it also means an annotation of literary work. However, it is often used in a title of a literary work when it is neither an excerpt nor an annotated version of another writing, and I guess that your two examples fall into this category. I do not know the exact meaning of 抄 in such cases.
Sometimes the use of 抄 in a title can be explained from the meaning “excerpt” even when it is not an excerpt of another work. There is a well-known collection of poems by Kōtarō Takamura titled Chieko-shō (智恵子抄) published in 1941. Chieko is the name of his (deceased) wife. This work is not an abridgement of anything. The title may mean that this work describes some essential part of his wife, but not her entirety.