Coercion, violence, and threat of violence is what "hierarchy" means.
A "doctrine of legitimate violence" is a (cynical) minimalist definition for the term "politics".
And laws and "enforcement" of laws are violence.
If Law=hierarchy, then Law is violent, and Chaotic cannot have hierarchy.
I'll be honest, I'm not certain I understand this post, but I guess the difference boils down to devils obeying the law of the Hells because they believe it will improve their situation in the long term by offering opportunities of advancement, whereas demons submit out of fear of being immediately destroyed by someone more powerful.
For demons, might makes right. Any claim to authority has to be backed up by the ability to kill anyone who challenges you. For that reason the majority of demon lords throughout the Abyss are too busy fighting one another for dominance to make an impact beyond that plane, which is why only a small handful of the demon lords that exist are ever prominently featured. Lesser demons submit to the rule of demon lords because they'll be destroyed if they don't. However, most demon lords don't "rule" so much as they lay claim to a territory and anything in it without any interest in establishing formal laws or local leaders. They're more like the warlords of a Mad Max movie.
In contrast, devils can hypothetically enjoy great legal authority and power without actually being physically powerful (although they are usually rewarded with increased physical power by Asmodeus through promotion). The Hells is basically a single, cohesive organization with two major goals: oppose demon invaders and win mortal souls to their plane. If Asmodeus can be thought of as the CEO of this organization, every other devil in existence (that hasn't been exiled, like Moloch) is an employee who seeks a higher position. These promotions aren't handed out lightly, either, as they are evaluated by the Ministry of Promotions, one of several ministries in the Hells devoted to different subjects (such as the Ministry of Mortal Relations, which requires that devils summoned by mortals submit reports recording what occurred during the summoning). Unlike the Abyss, where stronger demons threaten others with immediate death to ensure obedience, the Hells actually has laws forbidding devils from physically harming one another unless they file for a license of lawful combat, after which they may battle in the Duelist Chasm in Stygia. Basically, every devil is a temporarily-embarrassed millionaire.