"'Kill him! Kill the umpire!' shouted someone on the stand;/And it's likely they'd have killed him had not Casey raised his hand."
These two lines best show that the desire to win at all costs makes people act desperately. In these lines the crowd has asked for the umpire's life out of desperation. They do not agree with the decisions he is making and think that the umpire will be the one to cost them the game so they start acting irrationally out of desperation.