There is an entire category for Google and has been for years.

No there was no google category at the time. Wayback machine and Archive.is has no record of such thing. ICANN WHOIS has the record of the web domain being less than 5 years old. The site never had Google site to start with until someone add it.

Editor notes show Google.com being listed since at least 2006. Wayback does not archive everything. The category has not always been exactly in the place it is now. Category names change categories are moved, are updated, etc. This category goes back to 2011, probably farther but I got tired of clicking next. Google.com has been listed for many, many, years.

Curlie.org is not as old as the original dmoz.org domain so of course it shows up as a newer domain.

Everything change, it took me a while to find google.com this site isn't user friendly. No one can find stuff easy and there is no log about when a page change. Everything in this site shows it is a new thing, no records of older stuff.

The records are for the editors and admins who work on the directory. Not public information. I had no trouble typing Google into the search on the front page of the site then clicking the category from the search results. Took me about 3 seconds including typing time.

As far as the length of time... this is a review of Curlie. Curlie took over from dmoz but Curlie itself (as a web domain and a directory) started in 2017. Before that it was The Open Directory Project at a different domain. This seems to be the cause of your confusion.

No one knows where anything goes, i had to guess how to get that infomation. Why was it ever a good idea to put google products first instead of google.com site on top. Also editing records shouldent be editors or adams, alternativeTo records can be seen by anyone.