The underlying publication from the World Health Organization on which the article is based seems to be "Depression and Other Common Mental Disorders - Global Health Estimates" and is available at the following link:
The numbers must vary a lot depending on the definitions you use. I mean if you include everyone who's depressed sometimes you'd get about 100% of the population and if you don't think it's a real illness you'd get about 0%. I suspect it becomeing the leading cause is more down to changing definitions than the world getting more depressed.