So for I gather you can load it like this:
1. Enqueue the CSS and JS
wp_enqueue_style( 'mediaelement' );
wp_enqueue_script( 'mediaelement' );
2. Add your markup
<video class="wp-video-shortcode" id="video-1010-1" width="190" height="240" preload="metadata" controls="controls"><source type="video/mp4" src="sample_mpeg4.mp4" /><a href="sample_mpeg4.mp4">sample_mpeg4.mp4</a></video>
The rest of the documentation can be found here:
Also the player doesn’t play mp4 videos for me.
Try safari, some videos play some don’t, it seems to be more a problem with browsers and video codecs…this one is out of the WP hands, imo.