I agree with the premise, but don't see (in this article, anyway) a connection between it and the idea that "ressitiment" [why not just, 'resentment'?] contributes to the continuation of privilege itself. The article seems to me to imply that people who are against privilege for a certain segment of society are to blame for failing to approach the privileged in a way that will get the privileged to help society end such privileging.

That is a common trope these days: to put all the onus on those who seek to improve society to find the right, proper, correct, etc. approach. In order to perpetuate the status quo those who resist change don't even try to deny or to defend this or that wrong, only to criticize the means that are being employed to try end it.