The post above does a good job of arguing for the American-ness of Death of a Salesman. Though I agree with the ideas expressed there and believe that this is a very American play, we can argue that some of the deepest themes of the play relate across borders and concern some basic principles of identity and humanity.
Though Willy's conception of success is definitively American, his struggle is universal: to be successful and to experience disappointment in that struggle. His family suffers along with Willy and this suffering is another universal element, akin to Oedipus Rex and The Bachae.
The play Death of a Salesman is saturated with "American" concepts. First, the theme of the play is "The American Dream." Willy's desire is to be respected in society as the best salesman who lives comfortably while providing for his family. This is the ultimate American Dream, to be "a self-made man." Being a successful salesman was one of the only ways that a man without an education had the opportunity to rise from poverty if he was trained and skilled enough in manipulating people. Willy's brother, Ben, serves as an excellent example of how a person can rise from poverty to wealth.
Second, Willy raises his two children, Happy and Biff, with this idea of "The American Dream." It is important for Willy to see that his children, especially Biff, are respected by holding down good jobs and establishing roots. Willy is constantly emphasizing to the boys how important it is to make their way in the world by working hard. This concept is extremely American.
Third, the play deals with the very real pressures the pursuit of "The American Dream" has on the individual as well as the family. Early in Willy's life, his job took him out of town and away from his family for long periods of time. Being on the road is lonely for Willy, and henceforth, Willy has an affair. It is not the actual affair that gives the play its "American" element, it is the represention of the sacrifices that is "American." This undying pursuit of "The American Dream" as well as the consequences of this pursuit (the affair) create the foundation for the dysfunctional family. A very common characteristic that often exists in trying to reach "The American Dream."
Last, the idea of disillusionment that Willy encounters is another aspect of "The American Dream." Through all of Willy's hard work to achieve this dream, he is left empty without successful sons, without societal respect, and without his dignity. Many people could relate to Willy not because of his profession, but because of this illusory American Dream.