You need to use the question tags to indicate the name and full version number of the story format you are using, as this can effect answers. I will assume you are using the default story format of Twine 2 which is Harlowe v1.2.4
When quoting existing examples it helps if you supply either a copy of that example or a link to that example, this helps those answering your question know exactly what example you mean. I will assume you are quoting the example found on the video Add an Image, Movie, Sound Effect, or Music Twine 2 wiki page.
I will also assume you are using the install-able release of Twine 2.
1. That wiki example is about to embedding a video file within a page, and unfortunately YouTube uses streaming technologies to supply the video content which means you need to use YouTube's video player (or a similar player) to play their videos.
You can use YouTube's SHARE > EMBED options (found just below a video's page) to obtain the HTML needed to display one of it's videos in your page. eg. The HTML obtained from this TEST VIDEO looks like the following.
<iframe width="560" height="315" src="https://www.youtube.com/embed/C0DPdy98e4c" frameborder="0" allowfullscreen></iframe>
... and the above can be pasted within a Passage will show the video.
In the case of displaying an actual video file (like those found here) the equivalent of the wiki's example would be.
<video src="http://techslides.com/demos/sample-videos/small.webm" controls></video>
... I added the controls option so that the Reader can choose when to start the playing of the video.
The HTML5 equivalent of the above would look something like the follow.
<source src="http://techslides.com/demos/sample-videos/small.webm" type="video/webm">
<source src="http://techslides.com/demos/sample-videos/small.ogv" type="video/ogg">
<source src="http://techslides.com/demos/sample-videos/small.mp4" type="video/mp4">
<source src="http://techslides.com/demos/sample-videos/small.3gp" type="video/3gp">
... which allows the Reader's web-browser to select which video file format it wants to play from the list of supplied, as not all video file formats are supported by all web-browser.
2. Due to current limitations of the install-able release of the Twine 2 application neither of the above video element based examples will actually display when using either the Test or the Play options, although the YouTube iframe element based example will.
note: All three of the above examples will work in both: the story HTML file created via the Publish to File option of any release of the application; as well as the Test and Play options of both web-browser based releases of the Twine 2 application.