First of all:
You’re referencing an forked version of the Zammad documentation from 2018.
I’ve contacted the owner of the docs to at least put a warning, he removed the docs.
Now to your topic.
The ticket state automatically switches from “new” to “open” as soon as the agent replied to the ticket the first time. A reply that counts in this regard is either an email or phone note.
More information on that topic can be found here:
From your screenshots it’s not clear what kind of article you created. My guess is that it’s a public note.