Sorry I dont know which tutorial your speaking of.
If your writing a Java App client/server, then it would definitely be router or firewall or both.
If your writing an applet, then you would have to run a webserver (I use apache, mysql, php Look at wamp
for an all in one install). This would be highly recommended for creating client/ server games over the web, just so you can test out what you create exactly as a user would see it.
I'm not sure about webstart programs (I would assume you would still need to run a home based webserver due to the communication of the program), I havent ventured into that area or had need to yet anyways.
Of course, as always, I could be wrong, but this is the path I took when I made a client/ server game.