It'll make them brilliant at music and maths.what kind of long term impact will it have on children raised this way in a western culture?
It might make them technically good at music, but from an artist standpoint they'd be mediocre at best.
This sort of parenting mode is using the piano and the violin to teach discipline, not music. As such, there's an extreme focus on the technical aspects of playing and a complete lack of the artistic side of things. Listening to someone trained and raised in this way play would be like listening to a robot and no one goes to see 14 year old robots play at Carnegie Hall. When I read this article a few days ago, I was flat out insulted by this corruption of what is supposed to be a form of artistic expression.
And on that note, what is fundamentally lacking with this sort of approach is any sort of nurturing of creativity which is a vital skill in today's modern world. Without the ability to be creative, a person will have extreme difficulty rising to the top in any given field. Science, engineering, medicine, software, whatever... the top people in the most important fields today need to be creative to truly make an impact. This sort of tunnel vision on discipline and measured academic and technical achievement is great if you want your child to learn how to be a cog in a machine, but that's about it.
This is a TED Talk from a few years ago and it's more about schools... but I think it provides a good counterpoint and demonstrates why creativity is so important: http://www.ted.com/talks/lang/eng/ken_robinson_says_schools_kill_creativity.html