There might be some type of Dish Network incryption that won't let this happen, but it really should be a simple as plugging the audio-video cords on the device into the audio and video Outs on the Dish Network DVR. You'll need some type of video editing software, Windows Movie Maker (PC) or iMovie (Mac). Navigate to the recording you want to transfer to your computer and click "Play." The video stream appears in the capture window in Movie Maker or iMovie. Click the "Start Capture" button in Movie Maker or the "Import" button in iMovie to begin recording the video stream.
Now, that seems pretty easy which means it probably doesn't work, but in theory that should be it. You might have to run it through a digital camera that has pass through capabilities.