Here's why it's the climax:
* High Stakes: The game is tied, and the Mudville team's hopes rest entirely on Casey's shoulders.
* Tension: The poem builds suspense as it describes the crowd's anticipation and Casey's calm demeanor.
* Dramatic Shift: The shift from Casey's confident swagger to his ultimate failure marks a dramatic change in the poem's direction.
The climax isn't just about Casey's swing, but the entire atmosphere surrounding it. The poem captures the feeling of a tense, close game, and the weight of expectation that falls upon Casey. While it's ultimately his failure that drives the climax, the moment itself is the culmination of all that came before.