You can use VLC ON THE MINI to open files anywhere on the network and stream them from there.
You can also use DVD Player ON THE MINI to open the VIDEO_TS file from a DVD mounted on another machine and play that over the network.
All you need is for the machine you wish to stream FROM to have Personal File Sharing turned on in the Sharing/Services System Preferences. You can then log on to that machine via the Finder from another.
E.g. if the machine name in the Sharing preference is Simons-iMac-G4, you connect to Simons-iMac-G4.local, using the user and password from that machine, and select which volume you wish to access - internal hard drive, that user's home folder, or any mounted optical disk, including DVDs.