From the other imbalances listed (like being up "the exchange"), I take it that they mean being up a pawn without having to give up anything in return. For pawn

From the other imbalances listed (like being up "the exchange"), I take it that they mean being up a pawn without having to give up anything in return. For pawns that is kinda obvious, but for more valuable pieces like a rook you can win it "cleanly" or maybe you take it with a pawn and then immediately lose the pawn. You can of course give up material for positional advantages as well, but from the article I don't think the author analyzed that. It would be difficult to accurately measure that anyway, some positions can be up +5 points according to the computer but only if you find 20 perfect moves in a row. Needless to say, most humans would not find those moves especially in the lower ELO brackets that the article analyzed.