Summary: Videoly is a content discovery service (which is allowed in YouTube's Terms of Service), not a video distribution service. Embedding video using YouTube embeddable player is totally allowed to online shops: a thumbnail that appears on the website is just a link to a video.
1. You can use video from Youtube as long as you use the player provided by Youtube. By that you comply with YouTube API terms of service. When YouTube users uploaded their videos, they granted all rights to YouTube. And when you use video from YouTube via standard player, it’s YouTube is playing video, not your website.
2. Videoly can guarantee that by placing YouTube videos onto the web shop, you’re not incurring any liability towards YouTube.
3. Case if video itself has been containing infringing content: YouTube itself does not claim non-infringement, they simply take down infringing content following copyright owner’s notice. If we become aware of concerns about the content which is not taken down yet, we shall stop displaying it in the Videoly widget anyway.