No disagreement with "words are weird". Just adds some challenges for all of us.
For the most part I think you are making progress.
Please remember that the target (Moonlight) computer must have a static IP assigned via your router.
If a "use port x" request comes in the router must know what computer that request should go to.
If the computer is using DHCP (dynamic) IP addressing then the computer's network IP address will change as devices come and go on your network. So the router will not know which computer is the target.
Using your router set up the "Moonlight" computer with a static IP outside of the allocated DHCP IP address range and reserve that static IP via your computer's MAC.
Configure the "Moonlight" computer's network adapter to use that same static IP address.
So when the router receives data the data is addressed to "Port x on IP address Y". The router looks at its information and knows that IP address y is assigned to "Moonlight" computer z and sends the information along via Port x. Moonlight then gets the data and does whatever it needs to do.
But if computer z is using another IP address (dynamic) then the router does not know what to do. Another computer may have the IP address, but its ports have not been opened as it is not set up for Moonlight.