Causative link not established. The NYT is (probably) the world's most successful legacy-newspaper business for many other reasons too. For example, its historic reputation as the paper of record; network effects and digital first-mover advantage; and America's need for a locus of media opposition to a bossy government.
The Washington Post is a national paper of record as well and it's in a tailspin; newsletters, games, and recipes are huge business areas of the Times.
There can only be one newspaper of record, that's the point. In a media landscape where everything became nationalized, the NYT leveraged its status to take the pot. Most of America's serious newspapers (Boston Globe, LA Times, Philadelphia Enquirer, all the rest) are now even more dead than the WaPo. The NYT, with its massive frontrunner advantage, did not need games and crosswords to win this battle.
> There can only be one newspaper of record,
I'm not sure I've ever heard this before. IIRC the term originates from liberians and can refer to papers of official record and reputational record.
The Wall Street Journal is highly profitable, and also definitely a paper of record.
https://libguides.mcmaster.ca/news/record