"Happy member of the domination club" should not be called "whiteness" just like "anti-intellectual attitude with violent criminal behavior" should not be called "blackness".

Yes, you can find examples where it matches. It's still perniciously misleading.

Domination behavior has been common among humans since at least 5,000 BC.

The Spanish conquistadors arrived to find the Aztecs and Incas each engaged in subjugation and domination of their neighbors. That the Spaniards went, "Ooh! We wanna play! We'll win, too!" doesn't mean that the dominator attitude has anything to do with whiteness.

It does have deep entanglements with patriarchy, though. (Patriarchal dominator societies have existed throughout the world among people of every race, regardless of how you feel like slicing humanity into races.)