The text of Hemingway's story says that the animal is a leopard, not a "white tiger." There are no tigers in Africa, white or any other color. This is part of the epigraph:
Close to the western summit there is a dried and frozen carcass of a leopard. No one has explained what the leopard was seeking at that altitude.
Hemingway should have known what the leopard was seeking, since he knew a lot about African animals. No doubt the leopard was following a mountain ram up the mountain. A leopard is the only kind of predatory animal that would try to catch a mountain sheep in its habitat. The ram probably stayed behind the females and their young, keeping just out of reach of the leopard and enticing it to climb higher and higher. Then when it had lured the leopard to a place where the animal had a bare foothold, the ram probably butted it and caused it to fall to its death. I believe this is a common tactic of mountain sheep and mountain goats when they are being stalked by predators.
I suspect that someone read Hemingway's story in a translation and got the idea that the dead animal in question was a white tiger.
The tiger represents an attempt at both purity and immortality. When Hemingway wrote this story, he was very concerned with his own lack of discipline and ability to write something honest and therefore, pure. Harry, who realizes he is dying of gangrene on the plains of Africa, represents an author who has "sold out" because he never took the time to write about things that really matter to him.
"His perceived failures eat away at him like the gangrene that eats his leg. At one point he explicitly equates them: ‘"Rot and poetry. Rotten poetry.'"
He has the pilot fly past the peak of Mr. Kilimanjaro because He
‘‘knew that there was where he was going.’’
Harry is like the tiger. Harry tried for some kind of immortality through his writing. However, like the tiger he fails to make it to the top.