Hi Henry,
I cannot reproduce your issue in my SharePoint 2013.
Create a new column in the content and set it as required and compare the results.
Add the content type into another library and compare whether the issue exists.
Check whether the issue is existed in other content type.
And I suggest you create a required field and add it into the content type and compare the results.

Best Regards,
Lisa Chen
Please remember to mark the replies as answers if they help.
If you have feedback for TechNet Subscriber Support, contact
tnmff@microsoft.com