My inclination is to leave it in, even if it's not on the spine / title page. It looks better on your list and it is after all the 2nd edition.
There's a similar situation with the 3rd edition (the-guinness-book-of-british-hit-singles-3), although it should probably be changed to 3rd edition rather than 3 as it is now.
It is written quite plainly on the front cover though, it's location dictated by, or as part of the design. Other than the authors names it reads.... The Guinness Book Of British Hit Singles 2nd Edition
I pre-ordered this at our local bookshop not knowing what an institution it would become.
The binding was not really good enough for a book that was going to be continually refered to and it's now practically loose leaf (but still complete). Should have ordered two!