To change the sharing permission for your media, navigate to the Sharing options window. Click the Media options icon next to the asset you want to share, and click "Share."
Here you can specify that you only want to share your asset with other admins. The asset will only be visible to the owner of the asset and admins of the Media Library the asset is contained within. Select "Share with myself and admins (Private)" from the drop-down menu. You'll see "This media is only accessible to administrators" at the bottom of the screen, indicating the change has taken effect.
When looking at the contents of a Media Library, private videos will have a 'Private' label for reference.