The following two passages may help to clarify Peirce’s admittedly peculiar usage of “formal” in this context.
We discussed that passage on Objective Logic a little while back, until we reached the customary fork of diverging interpretations. The relation between classical logic and its supposed alternatives is a current interest of mine but I can see no alternative except to view it from the classical side. This may be accountable to the way modalities, from impossible to possible and contingent to necessary, are viewed by the Platonic realist mathematician. What is possible is real and thus realized in the requisite space of possibility. So the possible may be surveyed, at any rate at the end of inquiry, in accord with the way its real extension rests arrayed under its comprehension. Of course you see the catch — “at the end of inquiry” — and there the rub must be left to its itch, for now.
But I cited that passage this time around only for the sake of collating its introduction, “Logic, in the sense of Normative Semeotic”, with the words of Peirce’s definition, “Logic will here be defined as formal semiotic”, giving us reason to say Peirce equates formal with normative in this frame.