Marlowe's Tamburlaine conforms, in my view, to the requirements of tragedy, though some features set it apart from similar plays of the period (those of Shakespeare and others as well as those of Marlowe himself). This is because the title character is a man for whom most audiences would have difficulty sympathizing.
Tamburlaine is a ruthless and sadistic conqueror. He fulfills the Aristotelian definition of a tragic hero as "a great man who has made a mistake," but his greatness consists only in his forceful single-mindedness and in his ability to command armies and defeat one powerful foe after another like an unstoppable juggernaut.
What mesmerizes us about Tamburlaine is, as always with Marlowe, the ultra-poetic lines given him to speak. A mere sample follows, and it's hard to choose any particular passage because all of Marlowe's verse flows with an uncanny beauty virtually no other playwright in English could equal (except, of course, Shakespeare):
Those walled garrisons will I subdue,
And write myself great lord of Africa:
So from the East unto the farthest West
Shall Tamburlaine extend his puissant arm.
The galleys and those pilling brigandines
That yearly sail to the Venetian gulf,
And hover in the Straits for Christians' wreck,
Shall lay at anchor in the Isle Asant,
Until the Persian fleet and men-of-war
Sailing along the oriental sea
Have fetched about the Indian continent,
Even from Persepolis to Mexico
To say that Marlowe had a way with words is a massive understatement. His use of place-names, many with an exotic ring to them, is especially noteworthy. It does not matter that the mention of Mexico is anachronistic. The beauty of the words is ironic in some sense because Tamburlaine is such a brutal, merciless leader.
It is a striking paradox that a character whose nature is so violent and whose actions are so destructive can speak as poetically as Tamburlaine does. And part of the allure of Tamburlaine is that in Marlowe's description he is (unlike the historical Tamburlaine) a "Scythian shepherd," a man of humble origin, who conquers a huge portion of what was at the time the "known world."
The requirement of tragedy that it generate pity and terror in the spectator is fulfilled in Tamburlaine, especially in the figure of Tamburlaine's enemy Bajazeth. Tamburlaine places the defeated Turkish leader in a cage and displays him like an animal, letting him out only in order to use him as a footstool, stepping on Bajazeth as he gets onto his throne.
The humiliation becomes too great for Bajazeth to bear, and he commits suicide by smashing his head against the bars of the cage. Again, it is Marlowe's poetry that gives depth to this situation, taking what might be seen as merely sordid and ugly and raising it to the level of tragedy.