I've finally gotten it to work for online multiplayer and...it's fun! I had to open up some ports though:
47624 TCP
2300-2400 TCP and UDP
More connection information is available here:
http://www.mektek.net/forums/index.php?s=&showtopic=156187&view=findpost&p=1219567
Make sure that Windows Firewall is set to allow them perhaps.
I've played lots of online multiplayer games and the only one that ever required port-forwarding was Sins of a Solar Empire (in order to host games) before a patch came out to fix it. So, I really don't understand what it's necessary for Mektek's release of Mechwarrior.
I think you need to copy the folder called "Pilots" in the folder called "Resources"