Yes you'd need to host or embed the video onto a landing page or website that you have ownership of, as you need to have the munchkin code on the website or links that you're looking to track. If the website link is beng properly tracked by the munchkin code, you should be able to select it in the drop down list of the ClicksLink on Website trigger.
Hope that helps
I think this needs more clarification on what you are trying to do. To me it sounds like you are looking to track a link on your page that goes to a Youtube video linked somewhere else. This should record the click activity regardless of where the video is hosted.