Well neither of the races we have are "races" anyway.
For there to be a distinct race there isn't a strict, settled criteria. But being of a different, sovereign political group is a trait that is common to all of them. Maghar and MU orcs are technically the same race. So are Zandalari and darkspear. Kultirans and Stormwindians. But they are are disparate groups of people, with their own governance, culture, themes.
"Wizard" is a theme, archetype. The Kingdom of Dalaran is a distinct group of humans who formed their own kingdom, with their specific style of governance, leadership, culture and themes. Just like the Kultiran were before them.