Though I really shouldn't have to write this, under Article V, passage by the Congress simply starts the process. Ratification by 3/4 of the states completes the process. The website you provided does a pretty good job of highighting this fact; providing a list of states that had acted on it and noting that the number approving it was insufficient for adoption.
Consequently, the 1810 proposed 13th Amendment was never actually a part of the constitution.
More recently, the Equal Rights Amendment (ERA) was passed by Congress and was sent to the states for ratification. However, it didn't get the necessary votes and failed. Would you have it listed as a "missing" amendment as well?
I never implied that it was, but if someone starts a thread about the "missing thirteenth amendement", it is probably about the proposed "Titles of Nobilty Amendment" that was proposed and erroneously shown as being part of the constitution in the US archives and in the compilations of statutes of many states in the first half of the nineteenth century.