You should look into the API: https://developers.google.com/youtube/v3/code_samples/
The code you posted only pulls the data for the current video and displays it on the page. It is working as intended.
EDIT:
I did some reading about the Google API, I found they had a perfect example to show you how to work with the data using jQuery. Here is the code, all I had to modify was the user to grab the video feed from. If you create an app that wants users to work with their channels you can use the API and get the key's needed, otherwise you can use the script below, it will load one video and thumbnails for the rest, it will let the user click the thumbs and load the video on your site:
<html>
<head>
<title>My Videos</title>
<style>
.titlec {
font-size: small;
}
ul.videos li {
float: left;
width: 10em;
margin-bottom: 1em;
}
ul.videos
{
margin-bottom: 1em;
padding-left : 0em;
margin-left: 0em;
list-style: none;
}
</style>
<script type="text/javascript" src="http://swfobject.googlecode.com/svn/trunk/swfobject/swfobject.js"></script>
<script type="text/javascript">
function loadVideo(playerUrl, autoplay) {
swfobject.embedSWF(
playerUrl + '&rel=1&border=0&fs=1&autoplay=' +
(autoplay?1:0), 'player', '290', '250', '9.0.0', false,
false, {allowfullscreen: 'true'});
}
function showMyVideos2(data) {
var feed = data.feed;
var entries = feed.entry || [];
var html = ['<ul class="videos">'];
for (var i = 0; i < entries.length; i++) {
var entry = entries[i];
var title = entry.title.$t.substr(0, 20);
var thumbnailUrl = entries[i].media$group.media$thumbnail[0].url;
var playerUrl = entries[i].media$group.media$content[0].url;
html.push('<li onclick="loadVideo(\'', playerUrl, '\', true)">',
'<span class="titlec">', title, '...</span><br /><img src="',
thumbnailUrl, '" width="130" height="97"/>', '</span></li>');
}
html.push('</ul><br style="clear: left;"/>');
document.getElementById('videos2').innerHTML = html.join('');
if (entries.length > 0) {
loadVideo(entries[0].media$group.media$content[0].url, false);
}
}
</script>
</head>
<body>
<div id="playerContainer" style="width: 20em; height: 180px; float: left;">
<object id="player"></object>
</div>
<div id="videos2"></div>
<script
type="text/javascript"
src="http://gdata.youtube.com/feeds/users/YOUTUBER/uploads?alt=json-in-script&callback=showMyVideos2&max-results=30">
</script>
</body>
</html>