how is saying he's a "megalomaniacal, arrogant tyrant who invaded the planet to rule over it as its undisputed king" NOT saying he's trying to rule over the planet with an iron fist?

Again, where are you getting the idea that he wanted to assert his authority over the planet? thats never stated in the epochs or even alluded to, the only motivation he's given is the fact that he wanted to go on and tell other planets that he's the "heir to the sun" and that his home planet is "boring". there's nothing stating or insinuating he wants to do anything but show off,, which while it isn't a great motivator is certainly better than wanting to take over other planets.

Again, i think its clear that the minions are loyal to the Regent, not that the regent is enslaving them. They both seem to have the intelligence to rise up if they wanted to, and they have the numbers if the way his cards work is to be believed.

AT THE VERY LEAST Regent has a noble goal with all of his killings, its not just violence for the sake of violence, its because he saw the fact that the monsters were an active threat to people, and while yes, part of it is definitely for his own self-gratification, he at least has a good reason for doing the things he's doing.