The headline says “White Anger.” Hillary never used that term—and if she did, then the article really should have quoted that passage of her book instead of the one they did. She also never says the “resentments” people felt weren’t important, and she never says she wasn’t paying attention to them.
Here’s the passage: “I understood that there were many Americans who, because of the financial crash, there was anger and there was resentment. But I believed that it was my responsibility too [sic] try to offer answers, not to try to fan it. It was a mistake. People didn’t want to hear my plans, they wanted me to share their anger.”
She’s not comparing the relative importance of different angers. She saying that she wanted to offer solutions for the problems that were inspiring the anger instead of simply stoking/fanning the anger for political gain. She also says that her approach “was a mistake” on her part. She misjudged the type of message people would want to hear. That’s all the passage is saying.
There might be a tinge of frustration in the last sentence. Or there might not be. We’d have to see how the passage reads in the context of the book. I know I feel frustrated that cogent plans didn’t win out over bluster and heated rhetoric that sought to blame an “other” instead of offering actual solutions, but that’s just me.
People can agree or disagree with Hillary’s assessment (that her time on the podium may have been better served feeding into anger than looking to provide answers for it), but to suggest that it’s simply a rant where she says she regrets ignoring a section of voters is a misrepresentation.
Separately, my understanding of the term “white anger” is like what @ragingloli described.
From what I understand, it’s not any grievance felt by anyone who happen to be white. It’s the kind of anger we can see exemplified quite dramatically by white nationalist/supremacy groups (but isn’t exclusive to them, unfortunately)—the kind of anger that claims that “whiteness” is under some sort of imagined attack, that diversity is a threat, that minority groups are the problem, etc. Ugly, divisive nonsense that deserves only as much attention as is required to get it out of people’s heads.