This is a game I a currently writing called Warheads3D, it is in the early stages in this vid, but I think is shows my GSM off quite well as well as my UDP/Socket Server/Client samples. In this game the networking is in a separate thread to the GSM.
Take a look at the vid here.
The vid is in 2 parts, the first shows all the menu currently written and some of the new effects in the GSM, the second part shows the game acting as a client subscribing to a web service so that game servers for this game can be visible to the client, the servers come on line one by one, some change state from accepting players to in game, and then some dropp off as they close down. The project so far can connect to the servers too, but as the game is not yet written I didnt think this would make for interesting footage, not that this does really, but it gives you an idea of what will be in the Beta of the GSM.
All the features you see in the menu system here will be available in the full release of the Game State Manager. If you want to take a look at the alpha then you can get a copy from my last post here
If you want a copy of the networking sample I am using in this vid you can get that here too.