The problem is in the ScrollViewer that is in the RadTileView's template - it handles the arrow keys and that's why the focus doesn't change. To workaround this you could remove the ScrollViewer or use custom ScrollViewer in which you override the OnKeyDown like this:
protected override void OnKeyDown(KeyEventArgs e)
{
    if (e.Key == Key.Left || e.Key == Key.Right ||
        e.Key == Key.Up || e.Key == Key.Down)
        return;

    base.OnKeyDown(e);
}