Yes, Christopher Marlowe wrote that. He was rather interested in Niccolò Machiavelli, and Tamburlaine (the play) reflects a bit of this influence, in the sense that it was a criticism of Machiavellian thoughts. His Tamburlaine (the character) can and has been seen as a sort of Machiavellian chivalrous mass murdering hero/villain, and the passage in question is spoken by Tamburlaine.
Marlowe, therefore, wrote his protagonist Tamburlaine as Machiavelli's idealized prince, a prince of heroic proportions with an iron-clad will whose sole virtue is glory for its own sake ... Marlowe understood that MAchiavelli had patternred his prince on the career of Timur ... Marlowe's Tamburlaine is "both Machiavellian prince and Scourge of God"; he is Machiavelli's Castruccio Castracani.
- Ashley, Susan A. Seeking Real Truths: Multidisciplinary Perspectives on Machiavelli. Eds. Patricia Vilches, and Gerald E. Seaman. Brill, 2007.
Note that the historical conqueror Timur who Marlowe based his play on, also inspired Machiavelli.
The impressive defeat by Tamerlane of the Ottoman Turks, who at that time were the greatest security threat to the Europeans, touched the imagination of nearly every European humanist, including Machiavelli, for whom Tamerlane's victory entered into the conception in the Prince "of the man who can rise to power by his own virtue."
- Heilke, Thomas W., ed. Published Essays, 1934-1939. University of Missouri Press, 2001.
That might be why the internet (mis)attributed this English quote to the Italian Machiavelli.