NYTimes is primarily ad supported, of course they were paid to publish it.
They issue quarterly updates on their finances which include how much they make from subscription (a bundle): https://nytimes.com/2018/02/08/business/new-york-times-compa...
This is not true.
"The company said on Thursday that it added 157,000 net digital-only subscriptions in the fourth quarter of the year, pushing overall subscription revenue to more than $1 billion for the year. Subscription revenue now accounts for 60 percent of the company’s total revenue."
https://www.nytimes.com/2018/02/08/business/new-york-times-c...
Which of these entities do you think paid the NYT to publish this review? Because that would be a major story.
Also, you shifted the argument. You asserted that "of course" someone paid the NYT to publish the review. Who did, and how did you discover this?
I don't get paid for writing my blog, and I've reviewed books that have probably only ever had ten readers. If they're really not getting paid either way then it shouldn't matter.
I will admit to a certain bias in placing reviews on the mental shelf next to certain forms of advertisement (I doubt the author purchased his copy of the book), but I am not trying to project that view onto anyone else.