Et tu, New York Times?
The answer is, and always will be, no. The web -- the glorious World Wide Web -- was created to share hyperlinked content, content not unlike your own! There is no feature I need for reading your content that the web platform cannot support.
I understand this is not the point. I understand you just want more granular tracking of me to help generate more ad dollars. If I was reading your content for free I would even accept this. But I already pay you for this content and you already serve me highly targeted advertising.
If you want to notify readers that you have a mobile app, fine. Show this message once or twice to make us aware, then stop badgering us. Or at the very least add a setting that lets us turn this notification off. The way you're doing it now is beneath your usual standard.