The State of Washington is a party to this case, hence, the Supreme Court has original jurisdiction.
Why the Acting Solicitor General did not go there Friday is a good question, as is the question of why this EO was issued before the DOJ team was in place.
Under the current jurisdictional statute, the Supreme Court has original jurisdiction only if both parties are states (e.g., boundary disputes).
It may be that the Left wants this to go the Supreme Court, get deadlocked at 4-4 and make a big stink about it in the MSM, with Soros-funded riots in the streets, etc. as a backdrop to the Gorsuch confirmation, rather than have this resolved in the government’s favor at the appellate level.