I'm generally weary of works that purport to examine the "season/game/play/drive/double-switch that changed the world". It's like the "Great Man" theory of history, and while individual agency and actors matter a lot, I think it ends up obscuring the broader societal trends that were really driving the action. I think that the single, discrete events in sports that have really changed the world are few and far between, and probably already covered to death.
That being said, I read this preview of Tim Wendel's "Summer of '68: The Summer That Changed Baseball, and America, Forever", and I didn't hate it. That's impressive, considering I'm sick to my dick of anything talking about 1968, the winner of the Boomer Generation's prestigious "You Just Don't Know What It Was Like, Man" award for 42 consecutive years. But this article, at least, focuses on what that year meant to some professional athletes, and those stories are interesting. It doesn't really argue that those athletes changed much of the Vietnam-montages-set-to-Jimmy-Hendrix-guitar-solos around them.
Instead, it indicates that the athletes were, just like everyone else, affected by the world around them. And if you- like me- spend a lot of time thinking and writing about how sports affect us, it's really useful to see the reverse, how broader society affects sports.
Sports histories aren't very interesting when they're a collection of scores and stats, and they're not very useful even when they include vivid descriptions of plays and games. But when they place the sports and athletes in the context of the rest of the world- in other words, when they're just a sort of context to help us understand what else was going on at the time- they're incredibly rewarding.