Well, this is quite odd. I restarted the network. This time, I got the same error message when testing connection on the Mac, but was able to connect and run things headlessly using Gizmo without a problem and despite the error message.
I am a bit confused about the port numbering issue. I manage ports on the router rather than on the individual computer, which, I guess, is how it's usually done. I am at work now, but just tested remotely the server settings on the three versions of JRiver that are on computers connected by ethernet to my router (a PC laptop, a PC desktop, and the MacBook Pro). The PC desktop gave no error message, the Mac gave the message that I mentioned (although followed by the message that sets out the access key and says the configuration can't be reached from the internet, about which I don't care), and the PC laptop is caught up in a "failure to update" loop that I will have to address by uinstalling and reinstalling. Anyway, given that the PC desktop connected to the same router as the Mac is working just fine and not getting the error message, I dunno what i ought to be doing about router ports at this point.