Based on the article, I gather that the racket shattered during play and the aluminum shaft was launched with enough force to impale her through her skull. The momentum behind tools like that is pretty significant and the cross-sectional area of a badminton racket shaft is very small. An adult skull is only around 6-7mm thick. Given she was a young child with a relatively thin, soft juvenile skull, I can see how it could impart enough force to shatter through thin bone if everything lined up perfectly.

Given it was a group of children playing, I wouldn't be surprised if the kids were also trying to smash the shuttlecock as hard as possible.

That was a lot of fucked up analysis. I'm going to go hug my cat and wife now.