Rui leads Team Hiragi and goes way back with Kaito and Tooru—they all went to the same middle school. Even as a kid, he had his sights set on beating Kaito, which pretty much shaped his whole drive. He's generally a good guy, but he's seriously confident in himself and his team's abilities. He's made it pretty clear that he doesn't really see Team Otori as competition, which tells you something about how he sizes up the field.
He and Eigo go way back—they're childhood friends, actually. There's this thing about them being called "Princess" and "Knight," which fans often bring up when talking about their dynamic.
Content compiled by AnimeList.moe from publicly available sources.