The reason is that your LayoutRoot is actually not "the" layout root when hosted in a SketchFlow player. Keyboard focus is initially on the Sketchflow player.
You might try adding a Focus() call in your page loaded event, but also make sure you have added the Jscript to initially focus to the actual browser Silverlight object first. e.g.
<script type="text/javascript">
function appLoad(sender, args) {
var xamlObject = document.getElementById('SilverlightObject');
if (xamlObject != null)
xamlObject.focus();
}
and
<object id='SilverlightObject' data= ...
[snip]
<param name="onError" value="onSilverlightError" />
<param name="onLoad" value="appLoad" />
If you don't have that code in the HTML/ASPX page hosting a Silverlight app, all keypresses go the browser instead.