It seems I've come across a narrative inconsistency. Spoilers ahead!
In one playthrough, the princess is revealed to be the Demon Lord and states that such title and power becomes inherited only after vanquishing the previous Demon Lord. Gallafrey then becomes the Demon Lord. Meanwhile, Gallafrey can murder the princess in another playthrough, albeit without knowing that she's the Demon Lord, yet doesn't become the Demon Lord.