The Boxee Box is made by D-Link and features an Intel CE4100 SOC.
It is quite similiar in function to that (security wise) of the Logitech Revue, or Gen 1 Sony Google TV boxes.
Here are two ways of rooting it:
Under Share Workgroup Name, you can simply add in another command with the semicolon.
For instance, to run "custom.sh" off of your USB Drive (noting to replace LABEL with the label of your usb disk):
;sh /mnt/LABEL/custom.sh ;
This will cause custom.sh to run at each bootup. The script can then simply launch busybox from usb, and spawn a root telnet daemon on port 23.
Scrape the two vias labeled in the picture, Solder wires to a UART adapter (TX/RX). Ground to any ground point. Once the box boots, it will drop you to a root shell.