Aside from potentially helping to identify if a session or cookie is worth 'stealing' (though I'd dispute it's validity for doing so), this method doesn't really yield any great benefit, unless someone is foolish enough to have user information in the CSS itself (as the blog post itself mentions). The only real way I could think of this being valuable is if, for example, the CSS defined some background image, or such, with a login, such as: www.yoursite.com/generateBackground.php?forUser=MyUser&withPass=MyPass - but in that case, you have far more comprehensive problems.
I'd consider this sort of 'attack' (I use the term very, very loosely here) to be a bit of a misnomer, as it's only about as useful as finding 'log out', or some other arbitrary string in some HTML (yes, I realise HTML/DOM-based XSS are largely protected-against). In either case, as you rightly say, it doesn't really help anyone, other than potentially giving them some hardly-useful information.