Why were parents not mentioned in Surah Al-Ma'arij in the context of the verses that speak of the sinner ransoming himself from punishment, while they were mentioned in Surah 'Abasa when speaking of a person fleeing from their relatives on the Day of Resurrection?

The reason why parents might not be explicitly mentioned in Surat Al-Ma'arij is the sufficiency of their inclusion within the family unit, as stated in His Almighty's words: (and his family); this encompasses both parents. The parents were not singled out for mention for the sake of conciseness. And "family" includes both fathers and mothers.