There is no equally simple version of Stockfish that is still supreme at winning at chess, but will easygoingly let you take a pawn or too. You can imagine a version of Stockfish which does that—a chessplayer which, if it’s sure it can win anyways, will start letting you have a pawn or two—but it’s not simpler to build. By default, Stockfish tenaciously fighting for every pawn (unless you are falling into some worse sacrificial trap), is implicit in its generic general search through chess outcomes.
The claim is pretty clearly intended to be about relative material, not absolute number of pawns: in the end position of the second game, you have three pawns left and Stockfish has two; we usually don’t describe this as Stockfish having given up six pawns. (But I agree that it’s easier to obtain resources from an adversary that values them differently, like if Stockfish is trying to win and you’re trying to capture pawns.)
The bolded part (bolded by me) is just wrong man, here is an example of taking five pawns: https://lichess.org/ru33eAP1#35
Edit: here is one with six. https://lichess.org/SL2FnvRvA1UE
The claim is pretty clearly intended to be about relative material, not absolute number of pawns: in the end position of the second game, you have three pawns left and Stockfish has two; we usually don’t describe this as Stockfish having given up six pawns. (But I agree that it’s easier to obtain resources from an adversary that values them differently, like if Stockfish is trying to win and you’re trying to capture pawns.)
Incidentally you have a typo on “pawn or too” (should be “pawn or two”), which is worrying in the context of how wrong this is.