The confession was actually written in 1677; however, because of persecution, was not officially endorsed by any Baptist. After the Toleration Act of 1689, the Baptists met together again to officially endorse the document.
Sometimes you will see the confession referred as the 1677/1689 London Baptist Confession of Faith. I have never seen it referred to as the 1688 Confession, and the seminary probably has a typo on their website.
The earlier Baptist confession endorsed by the a few of the same men who endorsed the 1689 was the 1644 London Baptist Confession. However, this document is quite different from the 1689, as it does not follow the model of the Westminster Confession.