While the newspaper does run ads, NYT's ad revenue is in large part driven by their 'native advertising' business (T Brand Studio).
It's a fundamentally different approach to advertising compared to what Google and FB are doing.
I think the problem is more that it's harder to quantify a carefully crafted brand campaign, and easier for middle-managers to look at a chart of click-through return rates and make decisions based on that.
I see this as the ability to test and measure beating out a better method that is less quantifiable. Basically the same thinking that leaves us with policies like No Child Left Behind where education has shifted from learning to test taking yet people are still under the impression they are the same thing.
It doesn't have more revenue than it did a decade and half ago.