The differences that you see in IE6 are just due to rendering differences for the various browsers out there. The tutorial is not necessarily intended to show you how to create a page or layout that is working with all browser versions, it is to show you the process for using and manipulating css to create the layouts.
I think that you could adjust the css of the layout to have it display correctly in IE6 using some conditional comments. What exactly you would need to adjust though I'm not sure. It looks like some of the elements may just be too wide to have both side by side you adjusting the width of either region would be a good place to start.
