But it means that the appellate decision will retain precedence, no? Wouldn’t losing precedence be the primary legal effect of overturning that decision? All case law that hasn’t touched the Supreme Court could theoretically be challenged, but most of it isn’t, and it’s considered the law until it isn’t anymore, right? How would this be any different?

The decision is binding only within the jurisdiction of the Court of Appeals for the D.C. Circuit.

So it’s not correct to say “because SCOTUS denied cert, Thaler is now binding national copyright law.”

Practically speaking, it is binding on the US Copyright office (one of the parties in the case) in CADC. And that’s important. But copyright litigation happens all across the country, while this ruling only directly constrains the relatively small number of cases within CADC.

Although this decision is not binding in other circuit courts, this decision still is something that you can bring to a judge in other courts. They are not required to follow this ruling because they are not in that circuit. However, they still will consider what other courts have said and that will be incentive to think hard before they do something different. A judge who does something different is generally expected to write up a reason why they did something different, and that's something that would be given to an appeals court if they do do something different for consideration of why the other court was wrong.

Yes, I didn’t imply national precedence. I imagine it would also signal to attorneys appealing cases other circuits that the same challenge will likely yield the same result.