We probably don't need to work too hard to convince you that Doctor Faustus is a drama. And it may seem pretty obvious to you that it's a tragedy as well. Talented intellectual signs soul over to the devil and gets carted off to hell—sounds pretty tragic, right?
But, at its time, Doctor Faustus broke a lot of rules about what tragedy was supposed to be.
For one thing, tragedies were supposed to be about great, super powerful people, like kings and princes. The idea was to write about someone whose destiny affected not just himself, but entire kingdoms.
Faustus just doesn't fit that bill. The Chorus even tells us he's born to parents "base of stock," in other words, to commoners (11). And despite gaining some fame as a magician, Faustus never uses that magic to do anything really important. Okay, sure, he rescues an alternative pope, Bruno, from punishment at the hands of the Roman pope. But the point of that whole episode isn't about the fate of kingdoms or Catholicism; instead, it's really about how Faustus amuses himself at the expense of others. Way to stay classy.
That's because the point of this particular tragedy is not to focus on the rise and fall of kings and kingdoms; it's to explore the battle for the soul of a single, relatively unimportant individual and to ask questions about sin and salvation as they relate to everybody, not just the VIPs. In fact, we'd even go so far as to say that Doctor Faustus has more in common with modern tragedies like Death of a Salesman or A Streetcar Named Desire than it does with King Lear or Macbeth.