Yes, to items involving ping and logging into each server, but for QlikView and NPrinting, I didn't think there was any extra port work needed. I thought I had read that inbound and outbound port rules were necessary for QlikSense, but I haven't read anything regarding ports and QlikView.
First of all upgrade to the latest version (currently NPrinting 17.3.1). I see you have referenced the 17.1 online help. There have been a LOT of improvements since the earlier versions including in how Connections work.
This is how I would troubleshoot this issue:
(a). Make a note of the service account used to run the NPrinting Engine service