Okay, I can understand where you are coming from. In some science communities, we end up with shorthand definitions for concepts that diverge from common definitions. There's even a term for this phenomenon: "jargon." When dealing with aerospace people, the rough properties of orbits are grouped into orbital planes. We don't really have a more generic term for the orbital plane where it requires little energy to maintain a stable progression that matches earth's rotation. In the 1960's we might have called it the "Clarke Belt." But I have never heard any aerospace person use that term. We all refer to it as the "geo belt" because that's the altitude where the biggest advantage is it is easier to remain stationary over the ground. You can also be stationary over the ground at any other altitude given enough energy. If someone is talking about the science or engineering of orbits, "geostationary" really only implies an altitude that exhibits some beneficial properties and not the more understood use of the word "stationary."

In this article, the author is using the term as in-community jargon. To differentiate this type of satellite motion, the author chose to qualify it with the term "retrograde" which implies an inverse motion.

In fact, I am currently working on a mission that will orbit the planet in the geostationary belt, but it will intentionally not match the rotation of the planet for most of its mission life.

Maybe as ASAT tech and other non-traditional mission profiles become more common, the community can eschew the "stationary" part of the term to better describe that orbital plane.

Also, don't let an aerospace person hear you refer to geostationary and geosynchronous as the same. I also made that mistake early on.

I've been hanging out with aerospace engineers for a few years. But, even with basic physics you need to remember: all velocity is relative to a point of reference. When dealing with orbits it gets so complicated that we have to be mentally agile enough to accept that there are many useful reference frames that all make sense depending on what you're observing. Most humans default to thinking in terms of ECEF reference frame so it can be hard to think of other frames and how the relative numbers are affected.

You're getting tied up in an earth orientation reference frame. Geostationary satellites orbit the earth with enough velocity relative to earth to sit over the same spot on the ground. Which means it has to orbit the planet once every 24ish hours. In an inertial frame, that's significant amounts of velocity. Going in the opposite direction means it will be traveling quite rapidly over the ground and still maintain a stable orbit at that altitude (or semimajor axis).