Keep app from opening when clicking a link
In Settings &rarr; Apps &rarr; NYTimes &rarr; Open by default:


Open Supported Links: set it to Ask every time
tap Clear Defaults


Tested on Android 6.0.1 and Android 7.1.2.

In Android 8 (Oreo®) you can also reach that setting via:


Settings &rarr; Apps &amp; Notifications &rarr; (Advanced) &rarr; Default Apps &rarr; Opening links


You can alternatively stop using Chrome since Firefox, for example, does not let you choose an app to open such links (if I'm correct).