I don't quite get what that lot of data to transfer in such a game should be. In general on each computer the entire map with all information is present.

So you have the choice: You could just transfer the player input and a turn based game which is kind of determinate by default should remain synchronized. Ancient modems are sufficient for that kind of data rate.

Or alternatively you compute some things only on the host or one computer and transfer the result. But even then, what would that heavy computation be? The AI only results in commands similar to players which are low bandwidth.

Maybe additional synchronisation information to make sure things still run fine but then you would be quite flexible in the amount of data transferred.

Would it be possible for Stardock to provide a utility which tests the system specifications and networking performance?

Such a utility could perform the same tasks as the game to verify if a system passes for playing Elemental multiplayer.  Speaking from experience with troubleshooting software issues, myself and co-workers will show customers its not the software from our company by verifying the server or client system has the same problem even when other software attempts to perform the same tasks. 

For example the software from our company will install services on the server.  If these fail to install we'll find some freeware software which also attempts to install services... naturally when the freeware software also fails to install services it's clear the issue is with the server itself ranging from permissions, registry, policies, domain accounts, etc., etc., .