How has Marlowe transformed Edward II, a chronicle play, into a tragedy?

Marlowe was no respecter of the status quo, and his plays reflect this. Modern scholars also believe he was gay, which likely drew him to the history of the unhappy Edward II, also presumed to be gay and presented as so in the play.
Edward's story becomes a tragedy in Marlowe's hands, instead of merely a chronicle of history, because the playwright sees Edward as not only someone who is foolhardy, rash, and totally unfit to be king, but as someone who is placed by fate in a position he's unqualified to fill. The tragedy is made more poignant by Edward's inability to see that his own actions have brought his fate upon him. He mourns his favorites:

O Gaveston, ’tis for thee that I am wrong’d,For me, both thou and both the Spencers died!And for your sakes a thousand wrongs I’ll take.The Spencers’ ghosts, wherever they remain,Wish well to mine; then tush, for them I’ll die.

But he never acknowledges the wrongs his mismanagement of the state have done.
In that sense, Marlowe created a very modern image, a flawed, yet articulate and passionate person, crushed by both his own behavior and that of the ambitious, ruthless people around him.