"I don't get it."
"Yeah, I guess the rules are kind of complicated, but—"
"No, I mean, I think understood the literal content of your explanation, but I don't understand how the behavior you describe could arise from the rules as stated. What stops teams from just cooperating with each other?"
"Cooperating? What do you mean?"
"You say advancing the ball to the other side of the field is a touchdown worth six points?"
"Yes, plus a point-after kick or two-point conversion attempt."
"So why don't the teams just take turns scoring touchdowns?"
"What? Why would they do that?"
"To score points. You said that was the objective of the game."
"Oh, ah—I didn't realize I needed to explain this part—the goal is to get more points than the other team. The team with more points is called the winner of the game, and the other team loses."
"So it's a zero-sum game?"
"But that's barbaric!"
"That's ... not usually the reason people call football barbaric."
"Lower animals fight over fixed resources, the power to create opportunities lying far beyond their abilities and even their concept-space. But you, living at the dawn of your world's intelligence, you have the rare opportunity to build new worlds—and share the proceeds between you. And you waste your energy on this contrived imitation of a payoff matrix that it is your birthright to supersede! It is revolting."
The zero-sum-ness, and the related preoccupation with sorting entities into a strict linear ordering, are indeed the reasons why sports constitute only a primitive form of culture.
(I had this insight the other day while thinking about chess, and how much less appealing the thought of taking it up again is in comparison to most of my other youthful interests.)
To state the obvious corollary: higher forms of culture can be viewed as versions of sports where interactions aren't zero-sum and involve the creation of more interesting data structures than arrays.
Football is a positive sum game, which is obvious from the fact that no team wants the other teams to leave the game. The football teams create a positive pie of profitable entertainment, in which the winners get only a slightly larger slice (at least in terms of $$$) than the losers. In fact, the positive-sumness of football is exactly the reason why the teams and players have to pretend so hard to zero-sum compete.