Well, he's been The Doctor only for a few hours (minutes?) at the end of his life. We know that during the Time War he's done quite a few un-doctorish things such as leading an army.
A similar case is the Ninth Doctor, who's been The Doctor for most of his life except the final moments when he broke the promise deciding to be "coward, any day" (in his words to the Emperor of the Dalek). But for most of his life he's been The Doctor, so he counts, while the "War Doctor" doesn't.
It's not as though the Doctors refer to themselves as "10", "11", "12" etc anyway. They are all just The Doctor.
That's just for us to keep them apart in our discussions.