Another answer which may be more to the point of your question: I don't think that the linked video makes a case for the people who would benefit from developing world aid literally being the viewer's family/friends. I think that the linked video makes a case for the people who would benefit being somewhat similar to the viewer's family/friends. It's certainly not true that the people who would benefit are literally the viewer's family/friends, but I think that most viewers with enough information would agree that the people who would benefit are somewhat similar to the viewer's family/friends.

I think that the video helps make this point salient to potential donors for whom it would otherwise not be salient on account of the psychic numbing effect which Paul Slovic talks about.