Although "Beyond" features everyone's favorite Cimmerian, Conan is not the protagonist. That honor goes to a young settler named Balthus. Balthus is one of a few brave settlers who has pushed over to the "wild" side of the Black River. Defended only by a isolated, pseudo-Roman military outpost, these settlers are on the far edge of civilization - surrounded by jungle and horror.
Howard is quick to draw comparisons between Conan and Balthus. Balthus is brave, noble and, ultimately, part of civilization. Conan is a creature of the barbaric other - no different from the evil savages & shamans that live in the jungle. And, when seen through Balthus' eyes, Conan is just as terrifying. Balthus, although heroic, is the outsider here.
This carries on into another major difference between "Beyond" and Howard's other Conan stories: the "good guys" lose. [Do you need a spoiler warning for something published 75 years ago? If so, consider yourself warned.] Not only do the evil outsiders overwhelm the fortress and drive out the civilized folk, but Balthus dies at the end. The lone, flickering candle of progress on the Black River has been extinguished.
"Beyond" is about civilization's brazen advance into the Great Unknown, and, more importantly, how the Unknown always triumphs. This short story encapsulates a gloomy, apocalyptic view of the world - how all progress is for naught, as mankind's natural, unavoidable, state is barbarism. In the telling, it is slightly less depressing (Swordfights! Panthers!), but not by much. Thematically, this is Howard at his most Lovecraftian.
In SF/F literature, we're taught that progress eventually triumphs - be it building an empire in Narnia or a city on Mars. "Beyond the Black River" says the opposite, which is why it continues to fascinate readers to this day.
[Random biographical note: I ran a version of "Beyond the Black River" as an Iron Kingdoms campaign. As a campaign, it was a little dodgy, punctuated by a few fundamental DMing errors (I allowed a broken PC & loved my NPCs too much. Still, it had a few high points (including a haunted asylum, added for no reason) and a few entertaining druidic tirades about the encroachment of civilization.
The Iron Kingdoms world is about the wild proliferation of fantasy industrialization. I liked the idea of a counterweight: a reminder that the uncivilized, brutal, natural world is right underneath the surface. Sure, a big fort may look permanent, but a gobber horde and a flood will take care of it pretty quickly.]