@phoneboy My uncle spent 40 years with United, and I'm very familiar with non-rev dress codes from having been a beneficiary of non-rev travel on both United and American (a friend's dad used to run American's LAX ground facilities). It basically boils down to "business dress." For kids, there's some leeway depending on the age of the child, as there should be, and the gate agent here totally blew it. And then their social media team blew it again.
Relatedly, my observation has been that non-rev passengers are usually dressed better than the paying passengers around them in first class and business due to the dress code.