Saying that you should learn the terminal because a machine may not have Atom or Sublime is sort of saying that an advantage of the terminal is that you don't have to install additional software, isn't it?
Nah, that sounds just like short for "I sometimes wear the devops hat" - that is, the author probably has to switch computers regularly. Productivity as a devops/sysadmin has different requirements than regular developer productivity. In the former case, you'd prefer standard terminal apps and default settings. In the latter, you'd customize the hell out of your CLI and editing experience.
Yes that's also key for network admins - ironically I found when doing my CCNA that my experience years ago on PDP's cli came in handy on ios (the Cisco os).
Eh, that doesn't scale beyond a few devices. There's out-of-band management, yes, but often it's in the form of an isolated management network, which allows automation quite conveniently. Even the serial console is often accessible over a network using terminal servers. You usually also want to be able to download and archive your device configuration automatically using eg. oxidized.
That said, being able to work with standard tools is extremely relevant for debugging problems, still.
There is a difference between pre-installed only vs being allowed to install apps, and CLI vs GUI.
There are many environments that are CLI only. That’s what the author is talking about. You’re talking about environments that don’t allow you to install apps. That’s a completely different discussion.