There are three elements of dominance: power, resources and status.
(Which is why Ex Cathedra's definition of Liberalism includes all three as targets of the dispossession agenda of the previous subalterns.)
While Whites --both in America and throughout the world-- still have massive ownership of resources and very considerable power, what we have lost is status.
Loss of status is just as fatal to dominance as loss of power or resources.
If you lose status, you lose respect, deference, your place in the hierarchy. At its worst --and we have it at its worst-- you lose your self-respect, your own belief in your right to live and thrive.
If you lose status, then your possession of power or resources is simply an accident, or even a crime, to be remedied by those who deserve to possess them.
Consider the status of wealthy Jews in traditional Britain post 1655 after Cromwell reversed the 1290 royal edict expelling them. Money they had, but the ruling classes considered them outsiders and aliens, socially and certainly maritally unwelcome. No status.
The irony of the White Privilege game is that only a group which has lost status would be vulnerable to that kind of critique to begin with and put up with it at all.