Yes, he is the "president of West Virginia" (note the deliberate case). This is pedantic, but that's rather the point when we're talking about legal interpretations. You started this subthread off with:
> How much trouble are they going to have by using "king of England" which is not a title that Charles III has or had, or has even existed for 350 years
You're right, they shouldn't have said "king of England". That demonstrates some ignorance on their part. However "how much trouble are they going to have?" Exactly none. There is only one country in the world identified by the name "England" (the United Kingdom), and it has one King, whose reginal name is Charles III. There is absolutely no other way this statement could be interpreted, and so it presents no legal trouble, correct or not.
Likewise if you flipped it around and said "the president of West Virginia, Joe Biden". That is very clearly referring to the current President of the United States, who by extension is also President in West Virginia (as he is in the other 49 states and territories). It's not the correct title, but it's still obvious who you are referring to.
It would resolve differently if the south seceded from the union again and appointed their own president who just happened to be named Joe Biden, of course.