here's their ToS, which is pretty clear about what you cannot do: https://help.nytimes.com/hc/en-us/articles/115014893428-Term... (relevant parts below)
Without NYT’s prior written consent, you shall not:
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(2) use robots, spiders, scripts, service, software or any manual or automatic device, tool, or process designed to data mine or scrape the Content, data or information from the Services, or otherwise use, access, or collect the Content, data or information from the Services using automated means;
(3) use the Content for the development of any software program, including, but not limited to, training a machine learning or artificial intelligence (AI) system.
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(5) cache or archive the Content (except for a public search engine’s use of spiders for creating search indices);