How did kinship affect being king in the time of Beowulf?

During the medieval era and prior, nations were not defined by geography but rather by how people were related to one another. “Kin” means direct family members. “Kinship” means who people who are related by ancestry or marriage.
The latter, “kinship,” is the basis for the Heroic Code, which dictates that a true hero will willingly, and without hesitation, confront death.
The word “king” embodies the ideals of both kin and kinship; a king is a head of a family of sorts. He must be a father figure. The relationship between kings and their subjects is sacred and both have specific duties and expectations.
Kings are obliged to:
Act in the interest of his people
Lead his troops fearlessly into battle
Materially reward those who fight
Be powerful peacekeepers
Subjects are obliged to:
Surrender all to their king, including their lives.
Avenge the death of a king or die trying
Subjects who fail in their duties will bring shame to their kin.
Here are some textual examples of the theme of kin and kinship in Beowulf:
Kinship and Kingship:
“And a young prince must be prudent like that,
giving freely while his father lives
so that afterwards, in age when fighting starts
steadfast companions will stand by him
and hold the line.”
A King’s Duty (Heroic Code):
“I shall gain glory or die.”
King’s Setting Example for Subjects:
“Behaviour that's admired
is the path to power among
people everywhere.”
Subjects Avenging Death:
“It is always better
to avenge dear ones than to indulge in mourning.
For every one of us, living in this world
means waiting for our end. Let whoever can
win glory before death. When a warrior is gone,
that will be his best and only bulwark.”
A Good King, Poor Subjects, and an Admirable Subject:
“Quickly, the dragon came at him, encouraged
As Beowulf fell back; its breath flared,
And he suffered, wrapped around in swirling
Flames -- a king, before, but now
A beaten warrior. None of his comrades
Came to him, helped him, his brave and noble
Followers; they ran for their lives, fled
Deep in a wood. And only one of them
Remained, stood there, miserable, remembering,
As a good man must, what kinship should mean.”
*Source: Unknown. Beowulf: A New Verse Translation. Trans. by Seamus Heaney. New York: W.W. Norton & Co., 2001.