Not a great article, IMO. Some points seem very weak. (Escalation? Escalation by whom?) The focus on international law is hardly relevant to how things are actually done in the world. I think the NYT does a better job of analyzing this incident.
My own thoughts: designating drug cartels as military targets rather than simply criminals seems like it could be reasonable. They're not less organized or less brutal than terrorist groups that have been designated as military targets in the past. Violence against them has the potential to make the world a better place, if that violence successfully disrupts their operations. With that said, having the President unilaterally designate them as such is executive overreach, and having Trump in particular do it is also likely to be a mistake in practice (or worse, an action done with no concern about being correct) even if it could be justified in principle. The shameless celebration of killing is a separate problem and both the symptom of and the cause of a more widespread moral decay.
I'm going to go against the trend here and say that libertarian corporate city-states actually sound pretty cool. They're generally not portrayed positively in fiction but I think they might work well in practice. I'm a lot less optimistic about cooperating with all my fellow Americans in order to govern the whole country democratically than I used to be. Choosing to move to an independent city-state with a government that I agree with (albeit one I don't elect) might work better.