Social comparison theory is the idea that our satisfaction with what we have isn't an objective measure, but is actually based on what we see other people have. Young people generally seem to have an innate desire to leave their hometowns and seek out what else might be waiting out there for them. When you add in globalization and media influence exposing them to what looks like a "better" life with more things, it's not surprising that they've seen ~9% of young people leave Bhutan.
The other question is, what will happen if Bhutan does increase their financial wealth as well as their happiness? Will they then see a net influx of people through immigration, looking for the lifestyle Bhutan promises? And will those new people be able to maintain the culture Bhutan has cultivated?
It sounds like the concept of Gross National Happiness is a successful one, on its own, but it brings new challenges that couldn't have been forseen originally. That doesn't mean they can't solve them without giving up their core values.