Since I have purchased the classic (i.e., original) edition before it disappeared from the store I cannot exactly check it for myself, but as I understand, to access classic edition you have: (1) go to your library, and open the page for BG:EE, (2) on the left hand side click on the "more" tab and choose serial keys (which can be used to obtain classic edition).

But hopefully someone in the meantime will confirm if that's the way to do it.

Thank you! I was expecting something in the containing folder or a separate download or something.