Is 13 years too old for an otherwise new-condition tire?
A 13-year-old tire may be rideable for a few years, but it wouldn't be fair to sell it as new. It just won't last as long as a new one would, and the hardened rubber will perform worse and possibly wear faster.

So, not necessarily "unfit for use", but definitely "unfit for sale as a new one". But depending on storage conditions and the tire, even a few years can make a tire unusable, such as obvious hardening or visible cracks.



As for the particular review linked in the question, it seems the buyer has misread the date code.

The page identifies the tires as Schwalbe Marathon HS. The Schwalbe Warranty Page has this photo of their production code:



The format appears to match the one in the question, but it still leaves at least two reasonable interpretations:


Day/Month/Year: giving dates of 20th July 2018 (question) and 26th September 2018 (warranty page).
Week/Year: giving dates of week 20, 2007 and week 26, 2009.


But, it appears that Schwalbe has changed their production code format with an extra digit in 2010 or so. Older sources, such as this recall from 2009 show a code that has only 5 digits before a letter:



Based on this, I'd say the format is Day/Month/Year and the date on the tire is 20th July 2018. It still makes the tires somewhat old to be sold as new, but not terribly so.