> Does it turn a blind eye? Does the NYT trick Google by displaying something else to Google then to me?

Pretty much this. Google used to have a policy called "first click free" that basically said "you can have a paywall, but a user must be able to see the first content they click on from a search result. for more content, you can make them sign up". They dropped that policy at some point (and it was never really enforced, though many/most did follow it), so cloaking for paywall-purposes is okay now.