Movies purchased from the iTunes store must be watched on your computer from within iTunes as your computer must be authorized to play content purchased with your Apple ID. It can't be viewed directly from your external drive using a different media player.
If you are running out of space on your computer, one option is to move your entire iTunes folder to your external drive. After doing so, launch iTunes while holding the Option key (Mac) or Shift key (Windows), select Choose Library, then navigate to the new iTunes folder on your external drive. Of course, if you do this the external drive would need to be connected to your computer whenever you are launching iTunes in order to be able to access your media. You can follow the steps under "Part 1" and "Part 2" under "External Drive" here: http://support.apple.com/kb/ht4527 to copy your iTunes folder to your external drive.