Hi Tony –
To pair the mobile app with the game, they both need to be on the same sub-net, which for most people will mean that they need to be on the same wifi-network. At that point, pairing should be pretty automatic, when you are logged in to both the app and the game using the same account.
If your game computer is connected to your network with an ethernet cable, this should work as well.
The key is that the router needs to be willing to route UDP traffic between nodes on the same sub-network.
One of our Zwift staffers lives in a big apartment building where he gets his Wifi as a building amenity through a service called Natural Wireless. In his case, he actually needed to book a service visit with Natural Wirelss, as explained in their FAQ about wireless printers. The issue, in case someone is facing something similar, is that Natural Wireless does not permit wireless traffic between nodes for security reasons. This can be overcome by buying a wireless router, and having Natural Wireless hook up a wireless repeater.
Hope that helps. If not, please book a support ticket, and we can try and sort it out with your log files.