Is the full-height newel post for this oak railing structural?
It's almost certainly not structural. Posts like that never are unless they've been installed by someone with no training or guidance. This seems to be a modern home, which makes it even more unlikely that it's structural. Depending on the home layout, there's a probably a beam or girder truss inside the corner passing over the post. 

That said, I'm looking through a peephole from the other side of the internet. The question is not answerable with certainty. Get some local help and provide appropriate access to the attic or other areas of the building.