If anything, perhaps optimistically, I think that Gaiman’s intent with the Netflix series has been to make the overall arc more of a cohesive whole. Using things like the Corinthian as a running throughline through the first half of S1 so that his role as the big threat of the second have is a culmination rather than a thing that happens, and giving him the agency to try to actively use Rose, Jed, and the Vortex to further his aims as opposed to only being related in that it gives an in-universe explanation for why all this random dream shit is happening around her. (And linking her to Hippolyta right from Doll House if things reach the point where we see them again.)
Part of it is the difference between binge TV streaming services and monthly comic book issues or even TPBs, but I do think part of it is that Gaiman is getting the chance to go back and write the story with the knowledge of where it’s going and how it ends. It’s fairly clear that the original work was largely written by the seat of his pants, and there’s certainly no shame in that, but the adaptation is letting him mindfully include themes and elements that were present from the start but perhaps not included consciously and certainly not with the awareness of how much of a role they’d play further on. (Gaiman has talked about some of the other ways the story might have changed, including a fundamental change to the way the series ends, that he included buildup for which never went to use.)
He’s also pretty clearly using the opportunity to make some changes to his stories with the benefit of hindsight, and Calliope definitely shows some of that. She has more agency in the show, taking the details the Triple Goddess gives her and realizing that Dream has escaped his confinement to call on him (rather than waiting passively for his release). It also makes Ric’s “inspiration” less graphic without making it too subtle to realize what’s going on (although, as @Aria 's linked article shows, still managing to be too subtle for some people. What really gets me is that this guy has obviously read the comics, where it’s spelled out in literal narration, but still apparently manages to miss this).
I also noticed that Calliope says that she’s going to try to change the laws that let her be bound in the first place, something that’s never even suggested in the original work. This actually strikes me as something that might be a big difference going forward, specifically when or if Game is adapted to the screen. The original work was always fairly clear that many of the “Laws” magical beings work under are unfair and unjust, but I feel like it’s a good thing to have it spelled out. Both because it makes the characters more seem developed to be aware of this, and to make it really clear that no the authorial intent is not behind the character who packs the most metaphysical punch.
I’m thinking about this in terms of Game specifically because, not too long ago, people were trying to use that story as proof that Gaiman had either “gone woke” or been bullied into appearing so by Wokedom and using Thessaly and the Moon as proof. (This was when they were also trying to TERFsplain to Rhianna Pratchett about what her dad’s opinions on trans issues would be.) I don’t think we should have to dumb down every piece of media for the sake of the densest or most bad-faith members of the audience, but while the trans representation and narrative in Game was frankly revolutionary for the time it is probably something that needs to be reassessed and reworked in 2022 on.