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?
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.
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.