The all-star
The all-star recruit, Taft Robinson, is a symbolic character who serves the school as a kind of hero figure. Their team needs him, and his presence on the team means likely victory in their division. He is a sports messiah figure who helps ensure victory, except against one other school. He must defeat a technical college to secure the championship. When he notices the parallel between his role and the role of the nuclear bomb in the pending Cold War, he gives up sport and studies history instead. He is not a hero after all, but merely a confused witness of human competition and the deep roots of blind loyalty.
The End Zones
The title points to a symbol. The End Zone is both literal and metaphoric. As a literal symbol, it signifies victory by way of touchdown. This is where Taft excels, and he experiences it that way until his exposure to real fear of nuclear warfare and existentialist philosophy reveal another way of understanding the End Zone. He sees that the end of the world is also symbolized in the points, the competition, the concept of victory, and in the likelihood of human competition.
The Big Game
The Big Game is often discussed by the characters throughout the novel. Then, as current events unfold, they slowly begin to realize the inherent connection between sports and human warfare. Both are rooted in human competition. In this light, the Big Game becomes a symbol for the Cold War. They even have the same amount of letters, divided 3 to 4. War and game are thematically connected by this symbolism through the whole novel.
The suicide
When a coach commits suicide, that serves as a symbol for the meaninglessness of sports and competition. Not only that, but his existentialism indicates a true connection to existential meaninglessness. He sees that warfare is also meaninglessness. The suicide symbolizes death literally to the students, and in light of his death, the football season seems suddenly different, although it isn't. The suicide is also a symbolic reference to the common fate of existentialist philosophers whom the students study, and who commonly die by suicide.
Death and horror
The coach's suicide is also embedded in a motif of death and horror. The horror of the suicide is well-explored, but also, a small plane crashes killing the founder of the college. The horror of existentialism and absurdist philosophy comes off the page when the students consider the painful paranoia they feel about current events. Sometimes, the world seems perfectly doomed to them by the likelihood of thermonuclear disaster. The Cold War is less a real combat and more a hypothetical combat with the threat of death as the primary weaponry.