Alice won the duel because she is, in Malus' estimation, the purest representation of the power of the Bloodstars. Even without sight, she felt their presence. So strongly that she upended her life to better understand them. And now she is queen of what is, on paper at least, the most power Lurian regime yet to emerge. Divine ordination 101.
To those not familiar with the sticky details of her conversion, she was the nominal leader of the Pyrists. Pyrists believe that there is a flame of the divine inside of everyone. Stars are giant, hot, flames. The Bloodstars are giant, hot, divine flames that influence us from the inside. It is his (very much private and unshared with anyone—even her) belief that outcomes such as these are the Bloodstars are in fact making her an instrument of their will, and that she is effectively the Muad'Dib of Dwilight.
