The definition I'm going by is that a crossover is as a fan fiction in which either characters from one fandom exist in (or are transported to) another fandom's world, or more commonly, characters from two or more fandoms interact.

If I am interpreting this story correctly (and I haven't had time yet to read/listen to it completely), that's not at all what is happening here. It appears to just posit that a TV show named Glee exists in the Supernatural world, the same as McDonalds, or Disneyworld, or Shark Week might exist there. Is this not the case?