Yes, totally possible. Where the video is hosted, you'll just need an embed code. Once you have that, you can add it as custom HTML on your landing page. Any links to Facebook, LinkedIn, or Twitter are likely controlled in that embed code. Your code should look something like this: <iframe width="560" height="315" src="//www.youtube.com/embed/XXXXXXXXX?rel=0" frameborder="0" allowfullscreen></iframe>
Just drag a custom HTML element onto your landing page and copy the code in. That should work just fine.