I'm guessing that you have added this youtube video trough the widget in CkEditor, is that correct?
I believe that you need to resolve these controls in order to show the correct HTML Markup. You basically need to wrap your literal control in a placeholder like this:
<asp:PlaceHolder runat="server" ID="plcContent">
<asp:Literal runat="server" ID="ltlContent" EnableViewState="false" />
And then call following method to resolve the controls inside:
There is also an older article which explains this and has some nice examples: http://devnet.kentico.com/articles/how-to-resolving-the-inline-controls
Let us know if this helps and if you need anything else.