You can't print on Newzie because the application doesn't support this function. I've downloaded the available version then looked through the Help section as well as the Settings area. There was a tab called Keyboard where all the functions were listed, but there was nothing related to Print which means that function is not there.
However, since the software uses Internet Explorer's frame, right click inside where the news are found and then choose Print. You will have the possibility to print the synced content.