People can quibble over the number of incarnations if they want, but as far as "true Doctors" go, it seems obvious that he shouldn't really qualify. Because he never truly acted like a Doctor.
But isn't that just semantics? At the end of the day, Hurt is
the ninth incarnation of the physical being known as The Doctor.
He is, but we're specifically talking about renumbering, and no, the War Doctor is not the ninth Doctor.