> ...horror leaves readers or viewers with...a sense that, even though the story is over, we still have something to be afraid of.
Unlike in the horror genre, Beowulf depicts danger coming from a well defined source, and conclusively eliminated by the hero's actions.
Horror evokes existential dread, a [quasi-]supernatural threat against an unwilling [relatively] impotent protagonist, often with an ambiguous ending. The monsters may be terrifying to the Danes in general, but they are not the protagonists.
Action evokes willing combat, antagonist(s) viewed as challenger or threat to vanquish by a duty/honor-bound protagonist. Beowulf travels far to engage the heard-of horror, as challenge for pride and later protecting his people.
Beowulf sees the first monster as a voluntary challenge, the second an obligatory follow-up, and the third a duty. Any subsequent vague threats are just the way of humanity; this is not "and they lived happily ever after."
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