That sentence is taken out of context. I copy here the text of the full paragraph, which answers your question:
If the game is not to be played rigorously, according to the rules above mentioned, then moderate your desire of victory over your adversary, and be pleased with one over yourself. Snatch not eagerly at every advantage offered by his unskilfulness or inattention; but point out to him kindly that by such a move he places or leaves a piece in danger and unsupported; that by another he will put his king in a dangerous situation, &c. By this generous civility (so opposite to the unfairness above forbidden) you may indeed happen to lose the game to your opponent, but you will win what is better, his esteem, his respect, and his affection; together with the silent approbation and good will of impartial spectators.
In fact Franklin, distinguishes two ways of playing the game, with strict observance to the laws of chess or not observing them exactly. Whether you play one way or the other should be agreed by both players, and both players should be treated in the same way.
In the first case, with strict observation of the rules, a piece touched should be moved, a piece moved should stand. And you shouldn't point out the opponent's errors.
However, in the second case, where you play a more informal game, he recommends pointing out the other player's errors out of politeness and good will. This might be applicable when playing against a beginner player who is still learning the game, or a much lower rated one, during an informal game. But also when studying a position/opening/endgame with a colleague.