I am unsure if this is correct. We know only Nords actually shout in the game, but is it because the other races can't or is it because other races didn't live under the Dragoncult and therefor never included it as a part of their culture?
I'm willing to bet, anybody can use the Thu'um
But they have to practice under the Greybeards, or maybe even an 80year old Dragonborn could teach them all, but still, I think with enough practice, any race could do it.....