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First-party is when the provider of the data is also the owner of the property where that data was collected and used.

Google segments used on Google properties = 1st-party. Google segments used on other sites = 3rd-party.

NYT segments used on NYT = 1st-party. NYT segments can't be used anywhere else because they don't make them available nor do they want to.

In one case Google is retailing the ads and talking to purchasers. The content is subject to Google's review and approval. And, Google has all of the data (quite fine-grained, since that's all they do). Because there is a third party in the transaction (NYT, consumer, Google), it gets the name.

In the latter case, NYT does not share its customer data with google. NYT ad dept is responsible for the editorial and aesthetic signoff of all advertisements. And, arguably, less data collection overall because advertisement is not NYT's business strength.

It does not seem as if they will give others access to the data, rather advertisers can go directly to NYT and choose which segments to target.

this seems like a more than reasonable approach - actually relevant ads, not pedsonalised ads.