Again, I am not a physicist, hopefully one will come and confirm or deny. Because I would say at first blush, it would act the same. But upon further thought I

Again, I am not a physicist, hopefully one will come and confirm or deny. Because I would say at first blush, it would act the same. But upon further thought I came up with the following. If the ship were not moving relative to the earth which was moving as a constant velocity away from the ship at near the speed of light, the inhabitants of Earth would seem to age more slowly compared to those on the ship (or the ships passengers would be aging very quickly when observed by those on earth). With that if earth streamed the video it would seem to leave earth as a constant c and yet it would have to overcome the relative speed of the earth moving away from the ship. Thus, it would still come to the ship at 0.1% the speed of light but because time would seem faster to the ship passengers I posit that the video would play relatively slowly.