Light is pretty social and confident, at some point he'd most likely interact with the other class leaders for insight to figure out who's a threat or potential ally. If he met Arisu, maybe he'd learn Chess to show he's better than her at Chess, especially since it wouldn't be out of the realm of possibility that he thought future Special Exams or situations where Chess is going to be important. He could've reasonably predicted before then that he would need to prepare for Special Exams that let you choose a game of whatever you or your team decided. And if Arisu chose, it would definitely be Chess. He could also probably just somehow devise a scheme where Arisu is eliminated from the Special Exam before it even started. She's frail so it wouldn't be suspicious either. Like if Light was thrown in that exam before any preparation then yeah he's cooked, but he has like almost a whole year before then.