Christopher Booker lists this plot (not as a prequel, but
as the main story) in his
The Seven Basic Plots, and calls it "
Tragedy". He goes into great depth on the symbolism, but basically, it's the story from the point of view of the villain who is eventually defeated by the hero. It's also one step shy of his "Rebirth" plot, which allows
a woman or child to reach the villain's heart, get him to
turn from his evil ways, and
be redeemed. According to Booker, if the villain
repents but dies, it's still Tragedy, not Rebirth.