Isn't that kind of what the study says though? It specifically concludes:
> Moreover, recent correlational studies have confirmed that music engagement is not associated with domain-general cognitive skills or academic performance.
What I understand from this study is that whether you learn music or sit on your couch will have no difference on your cognitive abilities and only make you better at music if you do the former.
The study also mentions that you can't transfer skills to different domains. I think this further reinforces their conclusion.
> While human cognition has been shown to be malleable to training, transfer of skills appears to be limited to the training domain and, at best, other similar domains. [...] Near transfer – i.e., the transfer of skills within the same domain – is sometimes observed, far transfer – i.e., the transfer of skills across two distant domains – is rare or possibly inexistent.
While music can have positive effects, those would be mostly limited your general well-being, will not make you smarter and can be achieved through other activities as well.
> Music may be beneficial for non-cognitive constructs in children such as prosocial behavior and self-esteem. These possible advantages are not likely to be specific to music, though. In fact, any enticing and empowering activity may improve children’s well-being.