When you think of the rules that govern the Star Trek universe, you first think of the Prime Directive, which is broken all the time. The next rules are that Captain Kirk always gets the girl, and that any new crew member played by an unknown actor beaming down to the surface has a death warrant. And they probably wear a red shirt. But those last two rules only apply to the original series. John Farrier could come up with other obvious rules, but that's not what this video is about.
Believe it or not, there is an underlying philosophy that guides how Star Trek stories are told. Some of the nine rules governing the fictional universe may have been born of necessity, like how almost all aliens are human-shaped, but they have become incorporated into the framework of all the Star Trek movies and TV series. Some are contrary to the rules of our reality. Sometimes the rules are bent or broken, but that doesn't ruin the structure as a whole that makes this fictional universe so familiar and understandable to fans.
The Federation is not a democracy. It's a bureaucracy. It's a lot closer to the United Nations than the United States or a Westminster system of government. Notice that you never hear about Federation elections. That's because there aren't any--or any of real consequence. An established bureaucracy rules.
Another observation that I've heard elsewhere is that Star Trek (especially TNG) is a fantasy in which the main characters are employed in a high-functioning workplace with intelligent and honest co-workers who are team players. To an extent, Star Trek is an emotional comfort food who people who are otherwise in dysfunctional workplaces with bullies, manipulators, and idiots.