I suspect the writer chose the term “Newton’s gravity” because it’s an article targeted at a lay readership

....

The underlying assumption in both Newton’s and Einstein’s models is that gravity is infinitely variable in its strength/range character, i.e. at a given range, gravity’s strength can vary continuously and any value is theoretically possible. The experiment described in the BBC article tests this assumption of perfect continuity. The results suggest that the assumption is wrong and that gravity is quantised in discrete (i.e. discontinuous) intensity packets. -

Uhm, yeah, they failed spectacularly then. You just explained it much more succintly and understandably.