Analyzing videogame worlds isn't really a easy task, and most of the time it's just because there is nothing to be analyzed. While nowadays having a huge, living world in a game is just another thing the PR team won't shut up about and that leads to unnecessary books or comics tie-ins, that's has not always been the case.
In older, more simple, times a good setting, most of the time, simply meant that that the background looked nice. We never knew how the media reacted to the fact that only a couple of soldiers were send to deal whit a whole alien invasion in Contra or if the kidnapping of the president of the USA in Bad Dudes had any impact in
the diplomatic relationship between the US and Japan. Even if information like this is completely useless, it's non-existence creates a situation in which we know almost nothing about places we've been visiting for decades.
So today I'll over-analyze one of the most iconic places in gaming history: the Mushroom Kingdom. (also, sorry in advance for possible inaccuracies. I didn't spent that much time doing research, so everything comes from memory or quick trips to Wikipedia).
Let's start with the common knowledge: Peach is the princess of the Mushroom Kingdom and is constantly kidnapped by Bowser, the king of the koopas, and saved by Mario and Luigi, a pair of Italian plumbers from Brooklyn, but that's about it. Government system, external relationships, main religions, why the hell Bowser keep participating in friendly sport competitions with Mario and the others besides capturing Peach so often et
cetera are all things we can only speculate about.
: According to Paper Mario the capital of the Mushroom Kingdom is is Toad Town. Surrounding it are the many different climates that serve as the themes for the levels. Super Mario Bros 3 introduces the Mushroom World, a collection of eight kingdoms with their own kings, including the normal Peach's kingdom and the Dark Land, ruled by Bowser. The place where the events in the Land games, World and Sunshine happen could be part of this land or be completely different places. Mario is a Italian from Brooklyn ,but it's improbable that both the US and Italy exist somewhere in this world, so it's probably a parallel dimension thing.
: Peach is a princess, so it's obviously a monarchy, but we don't know of which type. in Super Mario RPG there is a chancellor that is the head of government,and that hint it's a democracy, but he is never seen again in any other game. there is occasional mention to the king and it's implied he has political power , so it could be absolutism or some mixed government. Bowser on the other hand has a much clearer position as both the political and military leader of the koopas.
above: absolute power? International relationship
: The Kingdom appear to be in peace with most other countries: Mario saves the kings in SMB 3 and Princesses Peach and Daisy are good friends for exenple. Perhaps the only country it's in war with is the one ruled by Bowser. The war between the toads and the koopas could be lasting years or even decades or centuries. Maybe that's the reason for the constant kidnapings of the princess: by marring Peach, Bowser would be legally the heir to the Mushroom Throne, ending the war. That is also one
explanation to him appearing in the sport series(besides they just not been cannon): the toads and koopas are in a period of unstable peace and and want to avoid a conflict at all cost, so thats give diplomatic immunity to Bowser to capture Peach and to Mario to throw him into pits of lava.
above: diplomacy Religion
: Not much is know about the toads religion. They seen to consider the passage of Rosalina's observatory, mistaken as a comet, a really important event, with its own festival. Considering the "comet" is the source of the Power Stars, it's possible that their religion is based around these stars.
Also on the subject of Rosalina: she is a apparently immortal being that travel the universe. She raises the luma, which consider her their mother and that grows to become planets, stars or even galaxies, so she is the mother of the universe itself. The passage of her starship is something considered sacred in the Mushroom Kingdom. Through this point of view she is the goddess of this reality.
Finishing, the Mario world in really interesting, you just have to read into things the creators never intended. Also, sorry again for wrong information, and for the overall pretentious tone of the text. You're free to comment on how wrong I am.