Arthur Miller once wrote an essay called "Tragedy and Common Man." In it, he talks about how tragedy - a form of plays in which the main character fails (and usually dies) because of his own mistake - has changed in the modern world. Tragedies used to be about kings and nobility - now they are about common men, everyday people.
"Death of a Salesman" is about an everyday man - Willie - and it is a tragedy. Willie fails in his life because of his expectations and his inability to see life for how it really is and to work for what he really wants. As a result, he has lost touch with the world, which leads to him being alienated from his family and to him losing his job. His resulting depression is what causes him to kill himself.
Miller wants us to know from the title that this will be a tragedy, because then we are prepared to look for certain details. By knowing that Willie is going die, we look for the reasons and the clues that lead to his death. Our experience is focused. We also have more sympathy for Willie, and can relate to him more. If we didn't know that he was doomed, then we might react less sympathetically to his behavior. We would turn our attention and or compassion to Linda and the boys more so than to Willie, and therefore the message of the story would be lost. Traditional tragedies - such as Shakespaere's Romeo and Juliet - went under the heading "tragedy" when they were advertised for the same reason. The playwright wants to get a specific lesson across to the audience, and focuses our attention through revealing the end result first.