Nda To Keep Me From Talking About Divorce?

This is what my -will be ex wife emailed me “Additionally, I need to remind you that you, and any affiliates or family members, are bound by the terms of a non-disclosure agreement with my employer. This agreement prohibits direct or indirect—verbal or otherwise—disclosure of any information not generally known to the public concerning private, personal, legal, or business matters of the Company, its principals (including Lin-Manuel Miranda and Luis Miranda), and their family members, friends, guests, colleagues, and affiliated entities. I, as an employee, am included under these protections, and any violation will be taken seriously and handled accordingly.”
Now I never signed an nda and I’m waiting on her to actually send me the damn document. So this is all I have to go on. She’s saying I can’t tell people about our divorce or post about it on social media. She’s being very cagey and protective because she had an affair with a coworker.

Based on this email excerpt, does this have standing? Am I “gagged”?