NYT Digital (the website) was a separate but wholly-owned company from 1996 until around 2007, merging with the newspaper as the new building opened. Pageviews in the mid 2000s were half a billion per month, with approximately half that going to the homepage alone.
IIRC, annual revenues for website advertising were $150 million in the late 2000s, damned good for a newspaper site. This was before NYT jumped onto the mobile and paid-digital-subscription bandwagons, which accounts for the $37 million revs. Adverts are still king, even on the website, and that combined with the homepage being half the pageviews is why you see the most expensive placements there.
While the rest of the newspaper biz has been slow to adopt, NYTD were actively educating the old-school news staff about FB, Twitter, RSS and other common or up-and-coming technologies. They have programmers assigned to the news floor, collaborating with reporters, to build topical databases, perform big data analyses, produce dynamic reporting and graphics and so forth. NYT are doing about as well as can be expected -they're a news organization, yes, but they've converted themselves into a technology firm from the inside-out.
NYT offers developers REST APIs for fetching newsfeeds and the aforementioned databases. Semantic Web is an area of research, and they're on a level with Thomson-Reuters, and to a limited extent Bloomberg. NYT's R&D department (originally attached to the newspaper, not NYTD) produces tools for latent semantic analysis of news, comments, etc.
When Twitter hit its initial growth spurt there were many predictions it would eat the newspaper business. It hasn't, in fact the news business relies on Twitter for distributing headlines and links. 140 characters and photo links hasn't eliminated the need for in-depth writing, analysis and professional photography.
Sure, the transition to an all-digital revenue model is their Achilles Heel. Most of the rev comes from the newspaper, and the demographic average is male, 40s and makes > $70K per year. Getting the younger generations to pay for news is the challenge.
I'm a former NYTDer. I still admire what they've done to adapt. I don't know how they'll survive the next decade, honestly. It'll take a revolution in paid subscriptions to get the younger crowd as part of the paid demographic. HuffPo was being eyed as the primary competition, for awhile, as an advert-only web operation.