@andrew, if the theme isn’t responsive, it won’t matter if there’s CSS for the video player to be. That’s because the elements the video is contained in won’t resize, therefore the video will stay the same inside the space. So building-in responsive CSS to the player would have no effect on the situation you mention.
@esmi even if I did do it, it wouldn’t confirm anything actually. All that would prove is that Twenty Thirteen does or doesn’t include the CSS to make the player responsive. The issue that needs to be looked at is that the WP doesn’t include responsive CSS for the player natively. I’m fairly certain this is true, since I’ve now tried on several themes. However, as I just pointed out, this doesn’t completely confirm it, as it could just be that the themes tested conflict with the built-in CSS and haven’t been updated for WP 3.6 yet. However, it seems likely from what I’ve seen that the player is NOT responsive as implemented by WP, but Twenty Thirteen adds CSS to make it so.
If you (or whoever) has to have hard proof before you’ll look into potentially improving WP, well, then I guess I don’t have time for that. Sorry for trying to help out.