To be on the safe, all emails should have a reminder that this is a game, and not a real communication from the FBI, before the content which is game-related.
This interaction is guides not only by 18 USC §912, but also by the DOJ guidance on what constitutes elements of personation under 18 USC §912 on how it is to be applied. It cites the case in which "by inquiring about passports, defendants pretended to be federal immigration officers."
SoThe burden of making it clear that this is not an impersonation is on you. So the reminder that this is just a game cannot be somewhere in a "small print" (or in a link or on the last page of a long email). The burden of making it clear that this is not an impersonation is on you.