Personally I don't feel that airing someones dirty laundry on a huge website is an appropriate venue. Isn't this exactly what support groups like AlAnon and therapy aim to address in a more delicate manner?
Dude, that's exactly what you're doing here. But your anger towards the author is a lot more mysterious than the author's anger towards her dead husband. If you're wondering why someone would write an angry comment on the internet that you think reflects badly on her, look inward.
I think it's a perfect place for it. Rather than kicking it into the shadows, in private sessions where you only hear these things if you specifically get off your arse and go there, instead you encourage wider discussion, and show other people who won't or can't go to those options that they're not the only ones having these issues.
Alcoholism and the destruction of lives is a depressingly normal story. It's hardly 'dirty laundry' (another term of shaming) in the context provided - the author wasn't point-scoring off her dead husband, and you weren't forced to read the article. Relationships have ugly sides, and by exposing that, we help people better understand their own.
Also, it's an opinion piece, in a section called The Opinion Pages with the section title Opinionator, and even the domain has 'opinion' in it. An opinion journal would be pretty dull if it steered away from social taboos. People read opinion pieces to get different views on things (sometimes heatedly emotional), outside of the supposedly dispassionate journalistic norm.
I understand your stance; perhaps at the very least she should have used a pseudonym to protect her husband's family and friends. With that being said, we are only being exposed to a portion of the story which she has decided to share in a certain way. There may be circumstances which she chose not to mention out of respect for her husband's legacy or her pride. What if her husband was not only verbally abusive but physically abusive? What if his friends or family blame her for his alcoholism or death? We don't know the full context driving her decision to publish this in NYT, so to immediately dismiss her move as inappropriate seems a bit callous.
Her story also might help other people watching loved ones deteriorate take action before it's too late, or may help people grieve following the death of a loved one under similar circumstances. This alone may be sufficient justification for her actions.