Hi,
If you Back up the location of the iChat Community (where this thread is) you will see that is inside the Applications Area.
However the are only two item in Applications.
iChat 5 and iChat 6 sever had a community as they were inside the OS relevant to that version community.
That means there is a Messages are within OS X 10.8.x through to macOS 10.13.x (High Sierra) as it is currently.
Mountain Lion's Link to the looking at the Messages filtered posts
OS X Mountain Lion
And High Seirra macOS High Sierra
The error message "Not Registered" is the only error message if the app cannot send something.
So you will see it if an iPhone or Apple ID has never been registered.
You will also see it if the other device is off line such as an iPhone losing power, being out of Carrier range or a mac being turned off for a too long a period such as a extended holiday.
You will also see it if the Mac has lost contact with the server.
In this case you will more likely see it for every Contact you try.
If this seems to be the case then Test.
On your Mac set the Receive At IDs to just be the Apple ID.
On Your iPhone set just the iPhone Number to Receive (And Send)
Back on the Mac start a New Message.
In the "To" spot type your iPhone Number in full including Country Code (it will not show your Your My Card from Contacts as you are not expected to Call yourself)
Send an iMessage.
If the iPhone does not get the iMessages than your Mac is not logged in properly.
You will probably have to Phone Apple Support.
See more here When the iMessages account will not Login
This can be long and drawn out but Apple ID issues are free to fix.
The issue you have is to move up the different level of Responders until one of them can access the info on the Server and see if your Apple ID when used by your Mac is blocked.
It is a device Specific issue and the same Apple ID can be used on other devices and in other Apps on the same computer.
8:00 pm Wednesday; September 5, 2018
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
MacBookPro 15" 2016 (High Sierra 10.13.x)
Mac OS X (10.6.8),
iPhone 6 iOS 11.x and an iPad (2)