So I did a little searching, and it seems that the Seagate uses its own special software, so it won't natively run Squeezebox Server, or talk to it at all. There is a way to modify the drive to work for you, but it seems a pretty complex: http://wiki.slimdevices.com/index.php/SqueezePlug#SqueezePlug_GoFlexNet_Image
Basically your Seagate is a little purpose-built computer, complete with a CPU and memory. It has an operating system that is incompatible with your Touch. You need to basically re-install a new OS (the link above) in order to make it work. This may be something more complex than you are willing to attempt.
Lots of people use an old PC as a Vortexbox. It is very simple to set up using the free software, and basically turns the computer into something similar to what a NAS is.... you could then connect your Seagate via USB and it would word as you originally hoped: network access from any computer, streaming files to and fro, and of course working with your Touch.