Unless they, you know, have internet access, some hardware to play around with and the ability to read.
Given that though, I find it rather hard to believe the North Korean government could pull off a cyber-attack like this all by themselves, especially when you take into account the effect of international sanctions and the North's very outdated technology (I remember reading they still use a 1960's crank-phone for communication through the DMZ).
My best bet is that the Chinese government gave them significant assistance in launching this attack.
DPRK has modern computers. DPRK has internet connections. It has smart people who did well in maths class and know how to program. It has very tight control on all of this, but it has it. Hell, if they needed some more off the shelf PCs, they could just wander across the border into China and buy some; the train crossing into Dandong was full of DPRK citizens going into China.
No clue how much truth is behind it, I just remember reading about it a while back.