I did not mean to imply that majority always creates privilege and power. S. Africa is one example where that was not the case. Colonialist were almost always the minority, but had the power.
To overcome the natural tyranny of the majority you need racism. Today, in America, white privilege comes from plain old majority privilege (as Peterson points out) and from racism (which Peterson has spoken quite vehemently against in other videos). It is from both. To use the term white privilege conflates the two and the distinction is very important.
Your point about severity of privilege or dis-privilege is quite true. In fact, on social media I often challenge people to a game. I name one black disadvantage and ask the opponent to name one equivalent white disadvantage. The ridiculousness of their argument is obvious quite quickly. (This technique also works quite well in reverse to expose false victimhood).
[I notice the same thing. It was in my Medium daily feed and I have "race" as one of my areas of interest].