to answer the question in the thread title:
every tcp/udp game uses a port number. no matter if it is internet or LAN (which is, technically, the same anyway).
the difference is, in a LAN environment you can send out "discovery" packets, they are broadcasted to all computers in a lan. if a host is open, it can respond and tell the client the port number the game runs on. so the user doesn't need to know the port. but still, the game uses one (or more) port(s) to handle connections.