Doctor Faustus is both a morality play and a Renaissance drama, since the two are not mutually exclusive categories of drama. The play shows a man selling his own soul for power when all the normal sciences cannot satisfy his quest for knowledge, and the power does not make him a wiser man, but a more foolish and proud one—therefore, it is a morality play. It also deals with Renaissance era themes—man's reaching for knowledge, questioning the superiority of man—and features many of the hallmarks of Renaissance-era tragedies (such as a character's downfall coming from a fatal flaw and their own psychology rather than from fate or God's will, as in medieval tragedy).
However, some have wondered about the theological implications of the play and how this relates to its categorization as a morality story, particularly since Marlowe is believed to have been an atheist with no big love for the organized church. Is Faustus tragic because he reached too far and this is wrong, or is he tragic because he was wrongly killed for seeking to reach beyond human limitations at all?
Judging by how Faustus wastes his powers with jokes and tricks, I would say Marlowe's interests are in presenting a morality story condemning such reaching, but not every reader has agreed and it is very much up for debate whether it is a straightforward morality play or a more subversive one.