OK, but then that's different. Because you were complaining that they were not differentiating between actual killed services and things that naturally reached their end of life, but in this case, the site is actually wrong.
It clearly says that it provided provided users with anonymous search, which gives the impression of something like DuckDuckGo or Startpage. But that's not what's happening, and I think that's worse than your original complaint.
> Note that SSL search does not reduce the data that Google receives and logs when you search, or change the listing of these terms in your Web History
The page you linked to is for "Google Search over SSL" and is not the same thing.
Searches performed at encrypted.google.com (not just google.com with SSL) were not available in any user-facing capacity in one's Google account. It did not store the search queries in user-facing history, and did not use those terms for future search suggestions.
https://support.google.com/websearch/answer/7631341?hl=en
and does not have anything more to do with "anonymous" searching