Final answer:
The Hawaiian belief in mana and the practice of royals marrying within their family to maintain sacred energy represents animatism, an animist religious tradition. Mana, a supernatural force, was integral to the legitimacy and structure of traditional Hawaiian chiefdoms and has even influenced modern pop culture, albeit sometimes through cultural appropriation.
Step-by-step explanation:
The set of cultural beliefs outlined in the student's question, where Hawaiian kings would wed their sisters to maintain a concentrated sacred energy known as mana, is an illustration of animatism. This concept of mana, a form of impersonal supernatural force believed to make individuals or objects sacred, is a prevalent idea among various religious traditions and is a key feature in animist religions. For instance, traditional Hawaiian belief held chiefs as god figures embedded with mana, responsible for their communities' prosperity. The significance and preservation of this sacred power, accomplished through practices such as the marriage of royalty among close relatives, strengthened the rulers' legitimacy and reinforced a social system organized around the chiefdom, where tribute flowed upwards, and wealth and government provisions were redistributed among the common persons.
Furthermore, the tradition of royalty marrying within their own lineage to preserve the sacredness of their bloodline is observed in other cultures too, such as ancient Egypt, where the royalty believed themselves to be deities. The idea of mana has even transcended its initial cultural bounds, extending into popular culture through games like Magic: The Gathering and World of Warcraft, which use the concept of mana as a form of energy or power, demonstrating the cross-cultural appeal of such animist concepts. However, this often represents an act of cultural appropriation, where original meanings are reshaped as they are adopted into broader contexts.