It is fun to play with moebius strips, but if you haven't got the time to make one and test what happens when you cut it in two (as happens at the end of the story) then the video below provides the answer, along with some other interesting properties of moebius strips.
So will Wind see her dog again? The answer is a bit tricky! Answers in the comments.
Escher used the idea of Moebius Strips in some of his designs; the one below is one of his most famous pieces.
This video is another great variation of a Möbius Strip theme.
Vi Hart is obviously a Harry Potter fan. She composed a seven movement musical tribute the the Harry Potter Series, called the Harry Potter Septet. Here is a video, from the Septet, of a of a song that uses Ginny Weasley's singing valentine from the Chamber of Secrets.
Here is more of Vi's Harry Potter music.
The New York Times printed an article on Vi Hart which can be found at this link.