Housman is actually saying that, for the athlete, an early death is a positive thing.
His poem is similar to the idea that "it's better to burn out than fade away." Housman explains that, if the athlete were to live to an old age, he would live to see others beat his records (his eyes "cannot see the record cut") and live to see his renown (or fame, reputation) forgotten ("runners whom renown outran and the name died before the man").
By dying young, however, the athlete will be forever in his moment of glory. He won't be alive when someone inevitably beats his record. Housman is saying that disappointment and corruption (old age and decay) are inevitable, but by dying young, the athlete avoids experiencing disappointment and corruption.
