Well it seems after reading the support FAQ that the diagnostic and other machine specific info. they are collecting are for single player issues. I don't believe those support methods would apply here. I'm not sure if there's a separate avenue for multiplayer support but I guess that's who i'm trying to pass this info. along to.
IMO, most of that boilerplate stuff at the beginning is the equivilent of "is your CD tray serving as a cupholder?" type things, so I wouldn't pay it that much heed.
Oh, don't get me wrong, it's very good to put it in there as there are a lot of people who don't have everything upto date and whatnot. Still, the really important bit is at the end where it talks about the Stardock Diagonsitc Tool and how to create a ticket.
I don't see why the support tool wouidn't gather the information they might need, even if it was off of one computer. No harm creating a ticket and sending it in for them to look at. Sure, they might ask for it to be run on both computers. But one really won't know what SD will say until one submits that ticket, no? 