If you have a Tabstrip with "tabPosition: Left" or "tabPosition: Right", and then you next a TabStrip inside it with "tabPosition: Top" or "tabPosition: Bottom", it appears to apply some of the styling/position from the parent left/right positioning, breaking the TabStrip, places the tabs one above the other in an incorrect position.
Hopefull this link will work, if not you'll have to paste the code below into a new Dojo: http://dojo.telerik.com/eWiHa
<!DOCTYPE html>
<html>
<head>
<base href="http://demos.telerik.com/kendo-ui/tabstrip/tab-position">
<style>html { font-size: 12px; font-family: Arial, Helvetica, sans-serif; }</style>
<title></title>
<link rel="stylesheet" href="http://cdn.kendostatic.com/2015.1.408/styles/kendo.common.min.css" />
<link rel="stylesheet" href="http://cdn.kendostatic.com/2015.1.408/styles/kendo.blueopal.min.css" />
<link rel="stylesheet" href="http://cdn.kendostatic.com/2015.1.408/styles/kendo.dataviz.min.css" />
<link rel="stylesheet" href="http://cdn.kendostatic.com/2015.1.408/styles/kendo.dataviz.blueopal.min.css" />
<script src="http://cdn.kendostatic.com/2015.1.408/js/jquery.min.js"></script>
<script src="http://cdn.kendostatic.com/2015.1.408/js/kendo.all.min.js"></script>
</head>
<body>
<div class="demo-section k-header">
<div id="tabstrip-A">
<ul>
<li class="k-state-active">One</li>
<li>Two</li>
<li>Three</li>
</ul>
<div><p>A</p></div>
<div><p>B</p></div>
<div>
<div id="tabstrip-B">
<ul>
<li class="k-state-active">One</li>
<li>Two</li>
<li>Three</li>
</ul>
<div><p>A</p></div>
<div><p>B</p></div>
<div><p>C</p></div>
</div>
</div>
</div>
</div>
<style>
.demo-section { width: 600px; }
.demo-section * + h4 { margin-top: 2em; }
.demo-section .k-tabstrip .k-content { height: 140px; }
</style>
<script>
$(document).ready(function () {
$("#tabstrip-A").kendoTabStrip({ tabPosition: "right" });
$("#tabstrip-B").kendoTabStrip({ tabPosition: "bottom" });
});
</script>
</body>
</html>