Your best best is to ask on the wine forums at winehq (it's the same people) or on the forums at crossover.
First, you need to make sure that you have real access to the LAN. Check your firewall, and make sure your not blocking any ports. Make sure that the port your trying gets used.
You can also experience problems with older games that try to access NICs directly or some such. However for most part wine just uses the network you have. It doesn't care if the packets are routed to the internet or 5 feet away. This could be very game specific.
Older DirectPlay games also have some problems. If you look at Anno 1602 for example you will find that dplay (networking) is a problem. see the bug report. There is a workaround. Download the dll files you need for dplay better instructions here and set them to use them by doing something like
WINEDLLOVERRIDES="dplayx,dpnet,dpnhpast,dpwsockx=n" wine 1602.exe
Keep in mind this is just one way to achieve this.