A regular army is the key,firearm and cannon technology was only part of the equation.
Firearms were absolutely vital, unless there was some huge geographic advantage that empowered the central government to enforce its policy across a large area effectively with limited delegation of fortifications and armed groups to vassals.
There's plenty of powerful centralized governments around the world during the so-called Middle Ages,
"more centralized" perhaps, but still feudal. They still had to trust fortifications and autonomous armed groups to vassals. The apparently stronger regimes usually had geographic advantages that are not very well represented in CK2.
But it wasn't really that centralized. The Roman empire trusted armies, fortifications and governorships to subservient lords just like any other regime did at the time. It had differences to European feudalism, but nothing critical in this sense. Constantinople's power waxed and waned depending on the emperor and the geopolitical situation, which is just as I was saying: a fixed centralization value unrelated to the king's person and the situation of the empire doesn't represent the period very well.
Which is a perfect example of the impossibility of so-called bureaucratic empires at the time, if they have no geographic features which allow the government to rapidly deploy strong force to constrain powerful vassals (like China).
a good number of Islamic states.
Or more broadly, middle eastern you should say. Governing traditions in the middle east were the same for all religions really. It's true that middle eastern central governments were more powerful, but this is because of differences in geography: Most notable middle eastern states were established by nomadic soldiers that commanded powerful mobile armies that could traverse the deserts, arids and steppes fast and quickly crush resistance by sedentary populations. So the power was in the hands of nomadic warriors that weren't dependent on fortifications (which were far less prevalent in the middle east). So while the regime was still feudal, a middle eastern king would have to win the trust of smaller group of people, his powerful tribal warriors, in order to govern, while sedentary lords couldn't hope revolt against such warriors, so their trust wasn't needed as much. Of course, there were times when the Middle east was fragmented and this wasn't true: but usually new nomadic realms would step in, either from the steppes or the deserts and reunite the middle east or large parts of it.
By the 1200s, the Kings of France have control over more than 50% of the kingdom with these areas under governors appointed at the King's pleasure.
Again, in theory.
Any one of those governors could hope to become an established lord if things got bad for the king at some point.