The attitude to death that is expressed in this poem is that it is better to bow out of life when you have reached the pinnacle of your achievement as a human in your chosen field. Living beyond this only allows your glory to fade and your exploits to be forgotten. Note how the speaker in this poem, addressing the dead athlete, tries to comfort him with these ideas:
Now you will not swell the rout
Of lads that wore their honours out,
Runners whom renown outran
And the name died before the man.
The argument of the speaker therefore is that it is much better to die after having gained success and recognition, rather than having to cope with aging and seeing your name forgotten, or outrunning renown. After all, glory "withers quicker than a rose." Dying soon after gaining it is one way of ensuring that the "garland briefer than a girl's" remains with you forever. Such a view obviously discounts the value that there is in aging and grappling with different challenges.