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Funny one this.
Video uploaded by a member to a private group...
But no-one can see it....even if privacy is set to public...thumbnail shows...but video says private and doesn't work.
Super admin can't see it....even the member who uploaded it can't!
after i saw your backend and frontend panel, i tried to replicate your problem like this :
1. Login on frontend using with information you gave in site info.
2. i browse all groups.
3. i opened group name "Family" which is a private group and there is a video in this group.
4. i clicked to play this video
5. video is not playing, it said "video is private"
6. i click on "Watch on Youtube"
7. it said "This video is private. If the owner of this video has granted you access, please log in."
so my conclusion : this issue is not about jomsocial but about your youtube video permissions :) maybe you can check it on your youtube account or video owner account :)