Hi, this theme uses the WordPress excerpt function to display a short excerpt of each post on the blog page and blog archives, with the full content displayed on the single post. We feel this is better from a design point of view and is arguably better for SEO purposes as it goes some way to avoid duplicate content.
The excerpt function strips out code from the post content including youtube iframe code, so this is why the video will only display on the single post.
Hope this information helps. If you need to show the full post content when viewing lists of posts, you may be better to look at another theme such as Twenty Seventeen or Twenty Sixteen.