Someone please fix this, this movie is very obviously a musical.

"music" genre is only for concerts and this sort of things. So, it doesn't apply here.

"musical" genre doesn't exist. It should be added as keyword, which is already the case.

So, there are nothing to change here.

If this is the case why are there thousands of movie musicals tagged with the genre "music"?

This is explicitely written in the rule. I quote : "The "Music" genre should only be used for concerts, music documentaries and any films in which music is a key plot element. The "musical" keyword should be used for musical films."

Feel free to report the movies that you think shouldn't have the "music" genre.

The movie we are talking about here is about the production of a Broadway musical, it seems like it would fit this definition of the genre of "Music"

It is about the production of a Broadway musical, but not about the music itself.

This explain why it have the keyword "musical" as indicated in the rule.

"any films in which music is a key plot element"

This is a movie with extensive scenes where people are working on writing and then performing music numbers. It absolutely matches the definition in the rule you quoted. The music is a key plot element of the film. To say otherwise is absurd and indicative of being unfamiliar with the film.