What they are doing is programmatically loading the movie that gets chosen at the time it gets chosen.
LoaderMax is a very good code library for doing things like this.
They start streaming the video from the moment you click the button. that way you don't have to load a bunch of unnecessary videos and you don't have to start loading all of them the second you're loading your main SWF.
General notice: from now on, I would like to ask everyone to put [AS2] or [AS3] (corresponding to the version of actionscript you are using on your project) in front of their post titles when the question is actionscript related! Please help us help you faster. Thank you.