That's XHTML 1.0 transitional, not HTML5 which simply uses <html> tag.
Learn about DOCTYPE stuff here:
Nice job, otherwise, to get a basic 3 videos at once per page.
To switch between multiple videos in one player requires good knowledge of Javascript (or a framework like jQuery) and the video.js API. You'll need to embed all 3, hide what is not playing, create some HTML so a user can select which video or maybe link 3 thumbnail images of screen shots. The you'll assign a unique ID per video and use the API commands (Javascript) to unhide and play the proper video based on the active ID.
Details on the video.js API here:
https://github.com/zencoder/video-js/blob/master/docs/api.md
I want to be clear, this is not novice level stuff.
Here is some code to demonstrate the video.js aspect (API usage), do not just copy/paste, edit to suit your needs and customize as you see fit:
Code:
_V_("example_video_1").ready(function(){
var myPlayer = this;
// EXAMPLE: Start playing the video.
myPlayer.play();
});
myPlayer.src("http://www.example.com/path/to/video.mp4");
//or for multiple vid sources:
myPlayer.src([
{ type: "video/mp4", src: "http://www.example.com/path/to/video.mp4" },
{ type: "video/webm", src: "http://www.example.com/path/to/video.webm" },
{ type: "video/ogg", src: "http://www.example.com/path/to/video.ogv" }
]);
This example uses the video.js API and is as simple as possible to show you the basics. The rest is up to you. I don't know your skill level as to Javascript so if you ask, "where do I put that code" or similar -- you need to learn Javascript before attempting this.
If you're wondering why I am using video.js it's because you referenced it in your above code, and I'd use it too! Good job there.