Well, as always, it's a question of individual perception what "race" means....and people can argue about the exact definitions all the livelong day.

We use all kinds of words in ways that can be called into question, after all. For example:

Black people aren't black.
White people aren't white.
North American Indian/Native American/whatever the hell you wish to call them aren't red.
Jews aren't necessarily religious nor are they necessarily of a specific genetic stock.
Muslims aren't necessarily religious either. I've met a few Muslims (people who identified themselves as such) who were also atheistic, but who still claimed to be Muslim, so for them it was merely a label of cultural origin.
Gays aren't all gay. ;-) Some are, in fact, a bit anxious or morose.
The USA Department of Defense actually engages in attack most of the time.

And so on... ;-)