This is one of the most fascinating and clear-as-day construction of a sport that I have ever seen, and it really makes you appreciate how much thought has been made into this designing this culture.
The demographics are the easy part-Baseball is the Yankee game, developed between NY and New England. In fact it took Union soldiers invading to actually spread it to the South in the first place. Puritan New England banned all fighting sports and "mindless recreation", but allowed ball and bat games, and for good reason.
First we start with the fact that baseball has a narrative of being "fallen from grace". Sure we may be America's pastime, but there was better order before us. Even in post-WW2 America baseball fans believed that it was past its prime, and its the clear manifestation of the Calvinistic fall from grace, in which The Fall of Eden bears heavy. Baptism may save us from that in Catholicism, but not in Calvinism.
Similar in vain is the baseball obsession with curses, which are generational and passed on to fans. You will pay for the sins of your ancestors. Bill Buckner was always going to make that error in 1986, it was determined 70 years before.
Time is eternal in baseball(at least before 3 years ago). There is no clock and so the construction of time is measured in action. This is why Ben Franklin a born and raised New Englander said things like "time is money". Games can theoretically go on forever, and it only ends when it is earned, likening Calvinistic rhetoric about salvation via labor.
Baseball is the perfect combination of individualism and collectivism. Each individual faces the pitcher alone, like how Calvinistic God judges you and only you alone, in which no personal responsibility can be levied onto others, but you still operate as a team. The theologically charged "sacrifice fly" shows giving yourself up for the collective.
Failure is built into baseball, it is the only game where failing 70% of the time is fantastic. This represents the Calvinistic obsession with moral failure, that no matter how much you try, you will fail.
Puritans hated excess. It is the reason why New England cuisine was made especially bland or why fashion was dry, etc. Baseball's unwritten rules about flashiness or why the muted white and gray are the most-often used choices for baseball uniforms, especially in the past, shows this.
The baseball is a circular diamond representing one's spiritual journey. The bases which form a square represent the current earthly elements of work and toil but to make it back to the diamond-shaped "home" is the end goal. The batter suffers, runs, dodges trials like pick offs against to reach salvation. In fact defense is much less error-prone and efficient because the defenders can prevent runners from reaching salvation much more often then runners can make it around.
The statistics obsession of the game shows a scientific rationalism, a product of Calvinistic thought. Things can be measured and observed with human reasoning, and it triumphs over emotional and romantic fervor.
Umpires are the representative of the hierarchal(head ump, then 1st base, etc, etc) church which intends to call out and strike out runners from reaching their intended salvation. This of course means that umpires, compared to other refs, receive a very large amount of abuse from coaches and players, they are rebelling against authority like what the Puritans were doing against the Anglican hierarchy. The fiery tirade of the player/coach is like the fiery sermons of Puritan preachers. Ejection is excommunication from the Church.
In Calvinistic thought, old age is associated with wisdom, if you made it to old age it was assumed you could be one of the elect. The baseball free market treats veterans very well compared to other sports which pushes them out more easily, and the GOAT of baseball is agreed to have played over 100 years ago. Compare that to basketball where every day old heads are made fun of.
The Puritans had a very strong sense of managing strong bursts of action with reflective downtime. In their politics for example most town election years or meetings were about 50% participation rate but when contentious issues rose every now and then that number shot up above 90%. Baseball has a very strong spectrum in this as well. Some innings nothing happens whereas others show intense bursts of action.
The Little League primacy of the township over the school(opposite in football) shows the New England obsession with loyalty to one's town. There is no such thing as switching Little League districts, you must play for the town. Compared to the rest of the colonies, colonial New England showed remarkable rates of lifelong residency and of course, it made the town system, something completely unique to that region.
Stadiums are meant to be places of sacred geography in which timelessness prevails. Compared to other sports, ballparks are just not changing a whole lot. Plus, ballparks are integral parts of the city/town, in relation to a Town Hall or Church which served as the basis for municipal government.
Sports gambling was the big no no in baseball reflecting a Puritan morality about bad vices. Gambling was banned in Puritan Massachusetts but absolutely loved in Aristocratic Virginia, who preferred horse-racing.
It's fitting that Puritan Boston vs Quaker/Dutch NY is the apex of baseball rivalry. On one hand is the Puritan, gritty, curse-ridden, humble Red Sox fighting out for another day and the other one is the unabashed Capitalistic, star-driven and motivated New Yorkers. Philadelphia + New York were the richest and most commercially-savvy areas of Colonial America thanks to the Quakers love of commercialism.
And that's it. It's the puritan game plain and simply.