So I've read a lot of answers and questions and still cannot make this work. I have enabled the compression (both static and dynamic) in IIS. I have added the lines in the web config of the ASP.NET MVC 5 app (even though I am not sure they are necessary). My headers are accepting Gzip Encoding. I even turned off the windows defender (some guy posted that his problem was with the antivirus software).
And still - IIS does not want to send me Content Encoding - Gzip.
I am running out of ideas and answers - so if anyone knows the holy grail.. please, do share!