This is... not really in disagreement with what I wrote, I think? I wouldn't call the first two sections horror, but the description of the terror that Beowulf and (later) his mother wreak on the inhabitants of Heorot is
quite horror, at least to modern eyes. The way the hall is
hopelessly haunted by this terror, much fallen from its glory days in ways that are plainly visible, and the inhabitants unable to escape their fate, is, separately, even pretty damn gothic-horror specifically (the extensive and detailed descriptions of pure carnage and its psychological effects are rather
not gothic-horror, but something else). The environs and inhabitants of Grendel's Mother's deep mire-home, for that matter—carnage and terrible monsters are all over in hero fiction, as with The Iliad's blow-by-blow slaughter on the battlefield, or Gilgamesh's forest-monster, but the presentation isn't like
that.
But overall, yes, it's not really horror because of the figure of Beowulf, who's basically Superman, and has the exact same effect on the story that introducing Superman to many horror stories would.
Pretty heavy horror motifs, imagery, et c., but structurally and viewed as a whole, not really horror. I agree that it's not best-characterized as horror, but absolutely see why someone would make the connection, and even think it might be useful to do so. Taking it as a horror-flavored hero tale isn't too far off, I'd say. "Superman wanders into a remote town terrorized by actual demons, and, predictably, easily wrecks their shit and saves (almost) everyone", maybe. The settings and premise are pretty solidly horror and are presented as such, but the story, not so much.
Though, again, I get little or none of that from the third act, which is totally disconnected narratively from the first two anyway, aside from also starring Beowulf. It seems far more straightforward to me, and reads a lot like, say, a biblical hero-tale—there's a monster terrorizing the countryside and murdering away much like Grendel, but we don't get the horrifying descriptions of wanton murder, but instead Beowulf's followers holding back and quaking in their boots while he saves the day. Though that one's hard to read with fresh eyes if you've read The Hobbit and/or LOTR, because it has so much influence on them, and I'm sure being familiar with them colors one's reading of that section, with the result that it's hard not to read it as proto-fantasy. The very voice of it even reads more modern and like something from that genre, in sharp contrast to the prior two sections.