As the person says, they have been out of the field. For better or for worse, this is the term the field settled on years ago to mean showing that a quantum computer can sample from the Porter-Thomas distribution more quickly than a classical computer, “beyond reasonable doubt.” (What I mean by the last bit is that it must be an empirical demonstration that matches the very well established theory.)
It’s maybe worth repeating: “Quantum supremacy” isn’t some gimmick made up by the authors of this paper. It was used as early as 2012 [0] by John Preskill, a well known scientist in the field. It has well-defined meaning in the research community: a specific experimental verification of a mathematical result which shows plausible rejection of the extended Church-Turing thesis.
This result may not seem like much to the average reader, but—provided it passes the muster of peer review—it’s a huge step of progress in the development of quantum computers.