- Calendar: You can buy an ad for one day, a whole week, the weekend, just Sunday, etc.
- Section: You can run your ad in the Travel section instead of Sports.
- Region: For national papers, you can have your ad printed in only one region--for example buying a full-page NY Times ad that is only printed in the papers printed in DC.
- Edition: Papers use to run a morning edition and an updated afternoon and evening edition. Some papers now produce a free thin version that is handed out free to commuters.
Big papers have also long offered ad campaign management services, where you work with their staff to optimize a campaign (including creative sometimes) to target the audience you want.
Broad content-based targeting kind of targeting we or the GDPR is talking about. The issue here are individually targeted ads that are only possible with computerized ad delivery.
At that point wouldn't all ads be targeted, to some extend? The only sites that would be in "trouble" is massive news aggregations sites.
Besides if you advertise in the NYT you ARE technically targeting people: namely NYT readers. Thats a demographic right there. And a lucrative one.