One clue as to why the olier dies--and is the only one to die--lies in the importance of the textual connection between the oiler and the correspondent as seen in light of the Naturalist perspective in literature. Throughout the text, the oiler and correspondent are an inseparable pair:
Then the oiler took both oars; then the correspondent took both oars; then the oiler; then the correspondent. They rowed and they rowed.
Again and again, "the oiler rowed, and then the correspondent rowed, and then the oiler rowed." The other variation of the pairing is that while the correspondent rowed, the oiler slept. The oiler "slept once more the dead sleep," as he and the correspondent did together on the occasion when the cook took the oars to spell them.
Since one of the tenets of Naturalism is that nature is supreme and all-powerful and completely arbitrary, Crane may be using the pairing of these two men--the absolute equality of these two men--to illustrate this characteristic of nature, that with nature being all-powerful and destructive, there must be death; being arbitrary, it matters not which must be sacrificed to death. In other words, of two equal men, it matters not which one dies.