So far i have created the local, single person version of the game...
Great, I would suggest to continue with the local multi-player version of the game ( even when it is controlled by the same "terminal" )
From there you may explore RMI to invoke the methods remotely. It should be much more simpler than creating the multi-player version and add networking.
What RMI does is to abstract the network connectivity and allow you to simplify the execution of remote objects call ( that is, it simplifies having to write your own protocol with sockets )