Okay so that embed code comes from the “share” -> “embed” dialog on a YouTube video. So that superfluous stuff is from YouTube and yes it can be purged if preferred. I like the way it looks borderless, and definitely want to be able to go fullscreen … so a simplified template could be more like this:
<div class="videoWrapper">
<iframe src="https://www.youtube.com/embed/PASTE_ID" frameborder="0" allowfullscreen></iframe></div>