I agree that rules (and rule changes) affect player actions. I just don’t call most of them “a reward” or “a punishment”. And without those you don’t have “rewarding” (“giving a reward”) or “punishing” (“giving a punishment”).
To me a “reward/punishment” is something unrelated. Suzy said a swear word, so Suzy gets no ice cream tonight. There is no connection beween swear words and ice cream. Ice cream is “a reward/punishment”.
So, 4 bag slots is a “reward” for using an authenticator. But most game rules aren’t like that. I don’t think it is possible to design a game as “a huge set of rewards/punishments”.