Emails + passwords that are often reused is the key more so than doxxing people.

Article says no financial info disclosed, though there are other ways it's potentially serious, besides PII like email addresses leaking. Every World Championship there are incidents or rumors about someone's opening prep getting leaked. I think something like that happened last year involving Lichess. Two anonymous players had a bunch of games against each other, no big deal, except the players turned out to be a WC contender and his trainer playing practice games. That is very valuable info to opponents.

Also, there are a lot of cheating reports and investigations on chess.com. If the evidence against someone is credible but inconclusive, it is kept confidential for obvious reasons. That is also potentially breachable. In the past, if the person was conclusively caught cheating, they'd get sanctioned or banned quietly (IDK if it's still done that way since the practice became contentious). That too could cause trouble if revealed (look up Hans Niemann cheating scandal). One could take the view that those old incidents are like the Epstein files and should really be released, but at the time the practice was to not do so. I won't weigh in on this here.

I guess there is also potentially private video there, like of people's bedrooms, since if you play in a big $$$ event there, you're required to keep multiple cameras running, again as an anti-cheat measure. But this is a bit strained.

Anyway, breaches are bad.