I agree and since the link doesn't seem to work for me, I can't comment on the article.

Perhaps learning music changes the brain in a way that is different than say, learning how to cook French food or to fix a computer?

Yes, but it's well known that certain kinds of changes are qualitatively different. There is a big difference between learning how to speak French when you are a child, versus someone learning in middle age. There are also big quantitative differences in MRI scans of people listening to music between those who learned how to play an instrument before the age of 12 versus those with no such background.

I find I code more quickly and elegantly when I'm listening to music - especially ambient music without a lot of sharp edges that throw me out of flow state.