That shyt is a totalitarian regime. It doesn't matter what Kim Jong Un uncle's was even planning on doing, what matters is what his ass was accused of. There's no difference between what the leader wants and what goes, so any possible crime, rather than any legitimate suspicions, is all that takes to execute someone and their whole family. They execute first, make up the accusations later.
Kim Jong Un's uncle and his whole family might have all been planning to overthrow the guy, yeah, but they could just as well have pissed him off in any other way. And the entire family is killed because they could possibly be guilty, even if there's no basis for suspicion: there's no need to prove shyt, if the leader says they're guilty, they are.
That's some Moscow trials shyt right there.