Khan's thinking and reasoning is explained without the need for any mental gynmnastics.
But this is NuKhan, so while similar to the Khan of the Prime universe, this movie distorted his traits and attributes. He now really is a superhuman, who does the whole cliched villain gets captured thing and his emotions are now supercharged and electrified like pretty all of the main characters. Which pretty much sacrifices subtle nuances, gravitas and presence for the new Trek Kahn villain. So while Kahn can act and feel threatening, you just have to realise how stupid and convoluted his plan is (and what was his plan after all of that; free his people, start a Klingon/Federation war or both?) and that just really dilutes this character no matter how threatening he can be.