I believe if you share your media files with Mint (Samba) and your Xbox is connected to your network, you can connect and watch your media with the xbox. I haven't tried this personally but have read and heard it is possible.
I just confirmed this with my son's XBOX and it does work, somewhat. It seems the only format it will play is AVI. You will need to setup a SAMBA share for your media on your Mint system so that the XBOX will see it on your network.
The instructions suggested Windows XP or better, so I installed Linux :)