I think the biggest shock in this story was how short it was (even by short story standards), compounded by the rather abrupt ending. That said, I really enjoyed it. I think Howard accomplished a lot with very little. The language was wonderfully evocative, especially when describing Gordon's reaction to the titular song. Hearing is (in my limited experience) an underutilised sense in weird fiction, where we tend to get wonderful descriptions of what the protagonists see - or occasionally feel - while hearing is usually limited to drips in damp caves or chanting cultists. If nothing else Howard made an excellent case here for exploring weird experiences through other senses (and now I'm wondering what could be done with taste...).
In terms of the actual story itself, again I thought Howard did a lot with very little. My immediate response to the introduction is that this feels like an epilogue or sequel to a more classic sort of weird story; that of the protagonists plumbing the depths of the earth and discovering unspeakable terrors therein. This is even a style of story Howard wrote quite a few examples of himself, with Conan, Solomon Kane and others. So maybe this was him taking a break from that and writing a 'what happens next' story.
I think Howard provides just enough here that I didn't feel like I was missing out by not having that first part of the story, but you were right to point out in the episode that there are some serious unanswered questions here, not least the nature of the relationship between Gordon and Casonetto. I read Casonetto's use of "friend" as not quite literal, but certainly suggestive of the idea that they knew each other well before the incident. I feel like they probably weren't as close as Gordon being Casonetto's manager as you suggested in the episode (but that's just a feeling): maybe they were associates or rivals on the opera scene? I think the idea of Gordon stumbling across Casonetto's secret lair at random would be too ridiculous - he'd have to have some reason to suspect Casonetto was hiding a dark secret, with the revelation of what that is being the climax in the Satanic ritual scene. I think if I did anything with this I'd be tempted to make the "black nameless winged being" some sort of entity other than Satan too, just to ramp up the 'weird' angle (with Gordon not really understanding what he's seeing and misinterpreting it as Satanism, a reasonable thing to do in the 1920s or 30s). Not that there's anything wrong with Satanism as a plot device of course, but it can sometimes feel a bit mundane. Although Howard showed here that he absolutely had the writing chops to make whatever was happening seem anything but mundane!
To be honest, the idea of a sequel or continuation to this story didn't even occur to me (despite the abrupt ending) before I listened to the episode, but you did a great job of convincing me that someone could make a great longer story out of this incident.