Hi there,
Thanks for that permissions.
I have checked this and it seems that, there are issues regarding the 'Restriction' of your YouTube API key. I have made some fixes on this path .../administrator/components/com_easysocial/includes/crawler/hooks/youtube.php and it working fine now. I have reported this issues to our developer and this fixes will be included in our next release version.
By the way, honestly, we really not sure how this "Restrictions" works, but i would advice you to not use these "Restrictions", as maybe it required you to put exact location on where those YouTube API key is used on your site.
Please give it a check and see how it goes