I don’t the know the legal term but what does loss of reputation have to do with money ?
A very negative article in one of the biggest news papers in the country should in of itself be considered damaging.
You have to prove *damage*. If not money, what damage are you going to prove? You have to show somehow that it lost something based on the reporting. Did the school lose students? Did it lose donors? What measurable loss did the yeshiva incur that it is suing for?
Intuitively, a series of stories in the paper of record is damaging to one's reputation, but you still need to be able to point to how you were harmed.
Again, IANAL, and my knowledge of defamation law comes from Johnny Depp memes, so take it with the same amount of salt you need to take NYT's reporting about yeshivas.