It is only binding precedent in the Ninth Circuit, it is less accurate to say it only effects the Ninth Circuit, since decisions have effect other than as binding precedent.
A circuit split is also a reason for the Supreme Court to take a case, so the Ninth Circuit decision, without being binding, makes it less likely that any conflicting decision by another circuit will be the final resolution of the case in which that conflicting decision is issued, which is an important effect at the other end of the process.
LinkedIn does plan on bringing this to the Supreme Court: https://www.law360.com/articles/1237505/linkedin-will-go-to-...
I always understood each ruling on the rungs up the ladder to the supreme court applied across the land until a final ruling was determined.
That said, it is not unusual for a court to look to rulings in other jurisdictions to decide a matter if there is no binding precedent in place. They are not required to, however.
It gets tricky with nationwide actors though.
Besides some specialized topics like patents and international trade, nationwide orders and injunctions are the sort-of exception, which are based on a courts local jurisdictional power over a non-local nationwide actor.
I'm not sure what the generalized name of the principle (beyond injunctions) is called (I've heard it as a type of jurisdictional overreach), but the presumption as applied here is that LinkedIn, being in the 9th circuit's jurisdiction, also adhere to the ruling outside the circuit, absent a contradictory ruling by a different circuit.
(One of the usual requirements for the Supreme Court to even hear a case is that different circuits have conflicting rulings on a matter.)
But it looks like the Supreme Court is about to seriously reign that nationwide power back soon, at least for judges issuing orders to departments/actors of the executive branch.
That's not a “usual requirement”, it's one of many factors that can weigh in favor of the Supreme Court exercising discretionary appellate jurisdiction (and it's one that weighs very heavily in favor of it, even when no other favorable factors are present, since federal law meaning the same thing everywhere is an important principle.)
How else would one read it? :)