There needs to be a path between the devices to record it. The DVD's output goes through the on-board sound chip or another sound card, I'm assuming. If this is anything like the typical CD drive, there is an analog audio cable that plugs onto the sound card, meaning the audio signal goes there. There's no way to get that to the Delta.
However, there might be a way to route the DVD player's audio output digitally (with CD-ROM ddrives, this is typically possible with the newer versions of players like Windows Media Player and Winamp.) Essentially the disk gets read like a disk drive and the data is streamed directly to a WAV device. If you can do this, you can route it to the Delta's inputs and outputs.