Yes, you'll have to put the older machine online, just for a few minutes, to allow these IE8 bookmarks to move over to Chrome. This shouldn't take long to accomplish & for the safety of your newer computer, you can always turn it off. Then your Google profile will update, and when you turn the new one back on, everything should be there shortly.
It shouldn't take being online long to transfer bookmarks, though I can understand & appreciate your concern about placing an older computer online. If only more folks felt the same........
This deal of transferring things from XP to Windows 8 is looking harder than MS makes it out to be. Used to be, one could copy the Favorites folder to a USB drive, and the newer computer would give the option of merging. It's been some time since I've done this with IE, though one you have these, your IE bookmarks & some other preferences will transfer to a Windows 8 computer from another, simply by signing in with your MS account. A Windows Easy Transfer cable was one option to move things from one version of Windows to another with, but there's also others, see link below. In your case, you could use an external drive, to include Flash drives. The advantage you have with this, is you can use your installed security on Windows 8 to scan the contents before transfer.
Google Chrome is far more flexible, everything will transfer, including extensions, such as adblockers, to another computer with any OS. As long as you're signed into your Google account.
Hopefully, this will be a one time deal & from then on out, you won't have to deal with this anymore.
And down the road, if you want, you can create a Linux Home Server out of that XP computer, as a 3rd backup option. You can place it much anywhere you wish, well out of your way, for this purpose. I have a computer that shipped with Windows 7, should I get it going again, may do that myself, as it'll hold a large SATA ll HDD.