whether or not the video is up does not affect them

This isn't true, we should always strive for accuracy in our words. You don't believe the murder's video should affect the victims.

Objectively speaking, the video can and does affect them. It's really straightforward to prove this actually.

Inform the victims that the murder's video is being shared online by racists and thugs wishing to incite additional violence. Have a medical doctor present while doing this. The doctor could then examine the victims for various physiological signs of distress.

You might argue that the same objective response could be evoked, even if the video were censored, by lying to the victims. I point out that almost all arguments against censorship hinge on the importance of truth.

In doing what they’re doing, they are rewarding the murderer.

The murder's goal was to incite additional murders. Do you believe that censoring these sites will drive their members to murder?