Paper rejected based on "informal review" - any point in appealing?
I'm going to guess that personalities are involved here and that you aren't going to win any fight you start. However, I think it would be appropriate for you to write to the editor asking for an explanation of "informal" review and how it is considered appropriate. You could mention that your paper seems to have been rejected not using "normal order" and ask, also, if that is appropriate. 

I doubt you will get much satisfaction, but it is just possible that they will re-think their process. This might help someone in future, even if it doesn't help you. 

But if it were me writing the letter, I would be polite and just ask for information and a judgment of appropriateness.