It's not working because of how Parallels accesses the physical CD/DVD drive in your machine. I have the same issues with drive access under XP inside Parallels; the virtual driver doesn't allow for most stuff like raw level data ripping, unfortunately.
Hope this helps...
bb
ps
If necessary, try this (although it takes longer): Use Disk Utility to make a CD/DVD master file (.cdr but you can just change that to .iso, it's the same thing) of the DVD on the hard drive, then mount it with Disk Mounter and *then* try to rip with DVDShrink or do whatever with it. This way you're bypassing the virtual CD driver totally. So, image the CD/DVD to a shared folder on the hard drive under OSX, then fire up Parallels/XP and point DVDShrink to the mounted image file in the options (just like choosing a physical drive/ISO image to use to install stuff under Parallels).
Takes a lot longer but, you may end up getting the results you want.