The IDE (or SCSI) cable carries all the data off the DVD disc. DVD movies are just another kind of data file (.vob is the extension).
When the DVD player software opens the DVD data structure, it tells the hardware decoder on the video card to take over some functions that would normally be provided in the software and performed by your CPU - kind of like how a 3-D accelerated video card takes over some functions to render the output from certain programs.
The DVD drive doesn't need a special connection to the video card - DVD video isn't like audio CD's (which are decoded by a digital-to-analog converter which is part of the drive, hence the special cable from the drive to your soundcard).
Hope that helps.