You should be able to access your control using the FrameworkTemplate.FindName method... first, get the ContentPresenter from one of the ListBoxItems:
ContentPresenter contentPresenter = FindVisualChild<ContentPresenter>(yourListBoxItem);
Then get the DataTemplate from the ContentPresenter:
DataTemplate yourDataTemplate = contentPresenter.ContentTemplate;
Then get the MediaElement from the DataTemplate:
MediaElement yourMediaElement = yourDataTemplate.FindName("vidList", contentPresenter)
as MediaElement;
if (yourMediaElement != null)
{
// Do something with yourMediaElement here
}
Please see the FrameworkTemplate.FindName Method page on MSDN for more information.