Hi,
Apple IDs still work as AIM Screen Names if that is what you are getting at.
However they do have to be linked to iCloud IDs.
So older @mac.com IDs that you might have been using in older versions of the OS need to be able to do a sort of 2 Step Verification on the Password.
The same is true of @me.com IDs not moved over to iCloud.
It's about that version of iChat being able to do it rather than the ID not working at all.
I have active @mac.com IDs in Sierra that do not work in iChat 5.
iChat 6.2 is the cut off.
However as you then clime the Messages Ladder (Version 7 through 10 in Sierra with two version eights along the way) then you lose some of the iChat functions.
Formatting the messages, (Different colours in Group chats and different Fonts and so on)
Video/Audio chat from the AIM and Jabber accounts
The Screen Sharing that was part of that.
The Sound effects linked to different people for different actions.
iMessages has had the function to Start FaceTime for Video and Audio Chats.
Later the ability to launch the Screen Sharing app from inside Messages was added which does include an Audio chat.
(i.e. Messages now launches outside apps for the iMessages account only.
This does force you to use the same ID in FaceTime as well as the iMessages account so people know who is calling.)
Ports.
Your Internet connection is effectively divided into 65665 ports
On most routing devices (modems and routers that allow you to connect more then one device to the Internet) can control these ports.
Normally the first 1024 ports are Open anyway.
Browsers use port 80 for example to fetch most pages.
Some use port 443 for secure logins (Apple does here for you to login to Post)
Mail uses many ports that are in this lower group.
It is common fro outgoing mail to go on port 25.
Incoming mail depends on the service provider but looking in Mail and the Preferences and using the option to look and Edit the settings tends to show you the ports each service is using. Ports 110, 443, 567. and 998 are common.
FaceTime uses these
https://support.apple.com/en-gb/HT202078
The iChat ones are in this Doc Using iChat with a firewall or NAT router - Apple Support
It does state it is no longer supported and it is not an easy read.
This page http://www.ralphjohns.co.uk/versions/ichat3/ichat3pics/Firewall3/PortsinFirewall .html has a table of ports and which are used by which service. It starts also with a very old pic of an earlier Mac firewall settings.
Since that version (iChat 3) things have changed.
Later iChats and Messages uses port 443 to login to AIM.
Port 5190 is still needed to transfer files and pics.
Port 5060 is not longer used.
Like the HTML protocol uses port 80 for Browsers various other internet items uses a specific Protocol.
iChat uses SIP (Session Initiation Protocol) meaning it had specific ports to use. Port 5060 is one of the range for that.
However many ISP (Internet Service Providers) and some Internet Backbone services tried to block SIP (it effectively allows computers to make "free" calls) and you then had to pay more to have the ports opened at the ISP end.
Apple's and Skype's answer was to use the protocol but force it into other ports
Apple used the same ones and the Video chat itself.
The text side of iMessages uses port 443 to login
It also uses port 80
Port 5223 is used to get feedback from the iMessages server as to who of your Buddies is On line.
As you can see this is a port that Jabber connections also use to login to some Secure servers.
As iPhones are effectively always On it make little difference as you can't see in the app who is on line until it fails.
Mostly this will be when an Apple ID is not available as the Mac is Off.
Anyhow...
The Mac Firewall has long been changed that it will open ports if the App is listed in the settings for the Firewall.
This also tends to include processes used by the app such as File Sending (includes pics) and the login process that strangely does not have Messages in the name.
Ports in a routing device can be set to be open in several ways.
If you are using an iPhone as well as a Mac it can be best to use the UPnP settings.
(Universal Plug and Play).
This allow a device to tell the router to open the ports and keep them open for a period after use.
It therefore says having to bother list each and every port that might be used.
A boring long piece about the different methods here http://www.ralphjohns.co.uk/page3.html#_ports
Again written about the time of iChat 3.
Most routing devices have improved the amount of control you have nowadays.
Summary.
Only the iMessages side will invoke Screen Sharing.
This means having an Apple ID that is iCloud Valid.
The Mac firewall will allow most connections without needing any specific setting.
If it does not seem to work then list the Messages App in the list.
Most routing devices which includes modems that can link to several devices by WiFi or Ethernet (Strangely those holes/plugin bit are also called ports) have a method called UPnP.
This allows the app on the device to tell the routing device to allow the ports to be open.
It also allows this to be used by Multiple Devices.
The Apple Screen Sharing app is part of Apple Remote Desktop (ARD)
See this table of all the common ports used by Apple TCP and UDP ports used by Apple software products - Apple Support
Then from an iMessages chat the Details "button" top right will start up the Screen Sharing app for you using the interlinked rectangles icon.
I would set up iMessages first and get the chat working.
Then see if the Screen Sharing will work.
I would tend to not worry about the ports for the moment.

9:50 pm Wednesday; September 20, 2017
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 10.x and an iPad (2)