It is important to first consider a couple of the basic precepts of existentialism. Essentially, the existentialist protagonist seeks meaning and order in a chaotic and meaningless universe. Similarly, the existentialist protagonist struggles with his own sense of alienation and isolation in order to define him or herself.
With these tenets in mind, it becomes quite obvious how these things readily apply to Hemingway's "old man" and the novel as a whole.
There is no reason or meaning to the old man having lost his luck at fishing; there is not sense or order or justice in the sharks taking his catch. Yet through the crucible of these experiences, the old man's character is revealed. Hemingway chooses to render the existential dilemma of alienation and isolation quite literally by having the old man first ostracized and then set adrift, alone, for three days in his skiff.
Though the old man does not, perhaps, find meaning and order--as exists in his beloved baseball box scores--he does seem to find an inner peace that will stave off his sense of isolation and alienation.