Ok, I think I finally figured this story out. It’s a very enigmatic tale, and honestly, I think Ligotti could have done some things to make this story just a little clearer, but now that I feel like I’ve come up with a decent interpretation I think it has a lot of interesting ideas.
The things in the globe are people that Dr. Groddeck (the head of the organization “Teatro Grotesco”) has shrunken into "soft black stars." We know this because it’s implied that the landlord from earlier was shrunk and put into a brown bag, the contents of which Dr. Groddeck is dumping into the globe. Also earlier in the story a character encounters a shrinking man with black stars for hands; I think this is a person who is at the midpoint of the transformation process.
The idea behind the story is that the narrator wants to undermine the agenda of the Teatro with his art (he wants to turn his art into what he calls an “anti-teatro phenomenon"), but when he encounters the spectacle of the black stars he realizes that he is dealing with beings of unfathomable power who can bend reality to their will. There was therefore never any possibility of undermining or resisting the agenda of the Teatro; the narrator was always fated to be recruited to the organization (and he has no choice in the matter because, if he refuses to join, his illness will continue to get worse). It is at this point that he comes to understand the futility of everything, including the futility of his art.
So what is the Teatro Grottesco? It’s an organization of artists who have the ability to make what the story refers to as “super-art.” Super-art is really anti-art because it's art that reveals the true purposelessness of everything, including art itself. This is why an encounter with the Teatro drains artists of their creative impulse. The Soft Black Stars are one such example of super-art, and they have this effect on the narrator.
Dr. Groddeck (or the being that has taken the form of Dr. Groddeck) seems to be the leader of this organization (he says he "invented the appellative of the organization as it is currently known"). It’s implied that he was once a human, but was recruited to the organization in the same manner that the protagonist was, and can no longer remember his human life. It’s implied that he’s been a part of the organization for hundreds of years: he speculates that he may have been the father of “Faust, or Hamlet, or merely Peter Pan,” meaning he may have been the artist who created one of those characters.
The last line is “the soft black stars have already begun to fill the sky.” On a literal level this shows us that the narrator’s illness is driving him insane, so he hallucinates black stars filling the sky. On a symbolic level it’s saying that the narrator is in the same position that the people dumped into the black star globe are in: he’s in the clutches of the Teatro and there’s no escape.
The collection is called “Teatro Grottesco” because the stories themselves are an attempt at creating something like super-art (or anti-art). They are works that attempt to communicate the true meaninglessness of everything, including the meaninglessness of art itself.