Is Death of a Salesman tragedy or drama?
There is no question as to whether this play is a drama. It is a drama. The question is whether or not it is also a tragedy. Drama and tragedy can and do coexist, with essentially all tragedy falling into the category of drama.
Drama is the broader category here and tragedy the narrower. The situation is akin to that of the relationship of rectangles and squares. All squares are rectangles, but not all rectangles are squares. All tragedies are dramas, but not all dramas are tragedies.
As in the case with rectangles and squares the determining factors are fairly clear. Are all sides equal in length? If so, the rectangle is a square. In our case, we will ask, is there a tragic hero who demonstrates some strength (moral strength) and fails through no fault of his own? If so, the play is a tragedy and Willy a tragic hero.
Willy does have some redeeming traits and some moral strength. He strives to succeed for egotistical reasons, it's true, but he also seeks to be an example for his children (he fails, but he tries) and to provide for his family upon his death.
Willy's weaknesses in the play outweight his strengths, but we can see Willy Loman as an average man with average weaknesses and average strengths. Seen in this light, Willy is not a bad person. He is not a poor example of what people are, what they do, and how they suffer.
As a representative man, Willy qualifies (marginally) as a potential tragic hero. Does he cause his own demise or suffer a fate that is out of his control?
To argue that Willy does not cause his own demise requires an energetic interpretation of Miller's intentions with the play. It is possible to read the play as an indictment of a system that shows no loyalty to those who helped to build it. Willy is fired when he asks for a different position in the company, though he worked there for decades. Willy is also smitten by a dream that he did not create, a dream of success and greatness which he inherited, effectively, from his culture. These two concepts combine to portray Willy as a man with no chance at simple happiness and moderate success.
Willy is an "all or nothing" person and this mentality can be argued to be derived from his cultural situation. If this mentality led to his death, and it did, and if it is not his own personal flaw but a flaw of his culture, then we can say that the play is a tragedy.
However, a more simple argument interprets Willy as being entirely complicit in the development of his flaws. He is not loyal. He is bent on a dream that he can give up, as Biff does, yet he refuses to relent in his "all or nothing" stance.
Seen in this way, the play is a drama and, technically, not a tragedy.