Is it mandatory to have Ubuntu Server 16.04 in order to install and work properly with MongoDB on Ubuntu 16.04?
No, it is not mandatory to install the "server" image to get MongoDB to work properly. It might be "recommended" but MongoDB will run just fine on the 16.04 "desktop" image as well.
Why is it recommended?
Because the "desktop" image includes extra packages (like a GUI/Desktop) that can consume resources. This can hurt the performance of things like a database. So for production, server-based images are usually the best way to go.