I'm not sure if this is what you need. An example is the live example on jsbin.com. In any case, I hope the following will be helpful. You can use the iframe method that youtube provides to play your videos. If the browser supports html5, it will display a video with it, otherwise with a flash. It also works great with iphone / ipad without opening the iphone / ipad app.
You can use the following code as an example < iframe class="youtube-player" type="text/html" width="640" height="385" src="http://www.youtube.com/embed/bIPcobKMB94" frameborder="0">
in the above example, the video identifier is bIPcobKMB94. You can change this identifier and show your video.
You can access your iphone as a live example here.
Additional Info for youtube iframe
YouTube HTML5 Video Player
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