I second this as a classic example of
advocatus diaboli[0] in order to find a hole/weakness/wrongness in one own's initial argument/assumptions.
Taking the Nietzsche quote[1] into the context of his work: "Jenseits von Gut und Böse (Viertes Hauptstück; Sprüche und Zwischenspiele, 146)" [Beyond Good and Evil; Fourth main part; Proverbs and interludes; 146]] your interpretation seems more in line with the book.
The inevitability of birthing/becoming a Monster oneself by fighting a Monster for too long is akin to staring into the abyss long enough until the abyss is staring into you. Melting away of cause and effect, the blurring, the reversing and finally the interchangeability/permeability - in this case - of the line between the object and observer (objectivism).
Nihilism (dissolution of all values, meaningless-ism) as a standpoint devours its subject who in the beginning is looking at the outside world all around - from the inside out in the end.
[0]https://en.m.wikipedia.org/wiki/Devil%27s_advocate
[1]http://www.zeno.org/Philosophie/M/Nietzsche,+Friedrich/Jense...
146
Wer mit Ungeheuern kämpft, mag zusehn, daß er nicht dabei zum Ungeheuer wird. Und wenn du lange in einen Abgrund blickst, blickt der Abgrund auch in dich hinein.