The Encyclopedia of Fantasy (1997) describes Howard's Hyborian Age and similar imagined worlds as "fantasylands" in contrast to the more serious, Tolkienian worldbuilding of "secondary worlds." This perhaps undercuts the quite serious world-building Howard did in places like his "Hyborian Age" essay but also obscures the fact that all world-builders (Tolkien included) borrow or are at least derive inspiration from history or other works of literature.
Still, it's hard to deny that the Hyborian Age tends to wear its undiluted influences or antecedents proudly. Perhaps not as totally as say D&D's Known World or some other rpg settings, but to a greater degree than Middle Earth or most other literary fantasy settings. I can't be too critical of these game settings as it allows people to get a handle on different lands or cultures quickly, but it does strain suspension of disbelief for some folks.
The Hyborian Age does those similar gaming settings one better, however. In what I think was possibly Howard's best world-building idea (at least so far as things to steal for gaming), the overall action and theme of regions come through, even when his cultural inspirations are less clear. Visiting different Hyborian lands may not just mean travel through history with Fantasy Vikings here and a Fantasy American Frontier there but travel through different subgenres or modes of pulp/adventure fiction.
In his Conan yarns he gives us Golden Age of Piracy adventure stories, tales of the Crusaders and the Outremer, Frontier stories in the vein of the Leatherstocking Tales, and a few stories recognizable as just fantasy in today's genre standards. He does this often by dispensing with a lot of the historical things that led to these settings and situations and just gets down to the action readers (and presumably players) are looking for.
Vague or passing homologies are all he seems to need to get going. He doesn't worry about establishing a Christendom or an Islamic World--or even really a Holy Land to get his Outremerish setting. He handwaves some former colonies (now independent) of Koth (which is vaguely Italic maybe, but hardly Imperial Roman and with a capital whose name is borrowed from the Hittites) on a borderland coveted by Turan, and he just describes the players, setting, and action in a way that the vibe of crusades and Crusader Kingdoms comes through, regardless of the background differences.
Likewise, "The Black Stranger" deals with pirates and a treasure, sure, but to drive home we are now in Treasure Island territory, he dresses Conan for the part:
The stranger was as tall as either of the freebooters, and more powerfully built than either, yet for all his size he moved with pantherish suppleness in his high, flaring-topped boots. His thighs were cased in close-fitting breeches of white silk, his wide-skirted sky-blue coat open to reveal an open-necked white silken shirt beneath, and the scarlet sash that girdled his waist. There were silver acorn-shaped buttons on the coat, and it was adorned with gilt-worked cuffs and pocket-flaps, and a satin collar. A lacquered hat completed a costume obsolete by nearly a hundred years. A heavy cutlass hung at the wearer's hip.
Does this undermine the essential Medieval character of the Hyborian Age? Probably! Does it weaken one's ability to think of it as a sustained and complete world? Could be! Does it make it clear "we're now on the Pirates of Caribbean ride, behave accordingly?" Yep!
I feel like this tool can be put to good use by GMs. Even ones that are more interested in setting consistency perhaps than Howard. Even small details can do a lot.