You can use the TinyMCE's custom plugins and configuration options that handles the specific Content Type and generates the desired markup. In your TinyMCE configuration, specify your custom plugin by adding it to the list of plugins to load.

You can also configure the plugin to listen for specific events and define the logic to generate the <video> tag when your ContentType is detected.

Here is the jeneral idea how you can do that.  

tinymce.init({
  // ...
  plugins: 'yourcustomplugin',
  // ...
  setup: function (editor) {
    editor.on('drop', function (e) {
      // Check if the dropped content is your custom ContentType.
      if (isYourCustomContentType(e)) {
        // Generate the <video> tag and insert it into the editor.
        var videoTag = generateVideoTag(e);
        editor.insertContent(videoTag);
      }
    });
  }
});

For more detail you can see the doc

Thank you, it seems like a plugin is the way to go. Now to figure out how to implement isYourCustomContentType :)