Satō argues that the culprit of these murders must be the same because the info about the shogi board was only published a couple hours before Genda's murder, so, to her, it's simply too early for a copycat to have sprung into action.
The relationships between suspects and victims:
Nishikido (1st victim of the shogi murders) was friends with Genda (2nd victim), but none of the three suspects (Hishinuma, Shoko or Mina) had met Nishikido.
Genda was the one who did these training sessions, originally. There originally were 4 members of the practice group—Shūkichi had heard rumors of the group as being comprised of remarkably powerful players. The members were Nishikido, Genda, Yūhei Kishimoto (the one mentioned in the previous chapter that wouldn't be joining the group), who had recently became depressed, and Sanji Uriyū (brother of Shoko), who'd recently become a pro player.
Kishimoto's depression was likely related to Uriyū's unexplained, sudden suicide—Uriyū had been very high spirits and was having a winning streak, and they'd even anticipated and celebrated a rise in rank. Mina had been hanging out with him, at the time. Uriyū was also possibly part of the fixed game circle, since he apparently had been summoned by the shogi federation at some point shortly before his suicide.
Genda, finding himself suddenly alone after what happened to Nishikido, Uriyū and Kishimoto, asked Hishinuma to join him, and he invited Shoko and Mina.
When Conan points out that there might be more murders and Yumi scolds him, he responds, "But if it were Shinichi-niichan, I'm sure he'd say the same, wouldn't he?"
When Hishinuma tries to tell the police where Kishimoto's house is at, since he doesn't remember the exact address, they see smoke rising from it. Satō and Takagi rush there while ordering the suspects to go back to their respective homes and wait there, and not to go out on their own because they might be in the killer's list, too.
Yuminaga reports that they managed to prevent the house from burning down completely, but Kishimoto got burnt to a crisp. While at first glance, it looked like he was dead before the fire began because of a lack of vital reactions, his rectal temperature hadn't descended too much—it was possible he might've been alive until shortly before the fire began. Takagi asks if Kishimoto could have been killed after Genda, and Yuminaga replies that Megure told him about the shogi board found there—a board lacking 3 legs, this time. Yuminaga notices Conan, and Takagi admits he slipped into the patrol car without them noticing.
At night, Shūkichi rings at someone's door and apologizes for his sudden visit, while commenting, "so this is where you moved to", implying this person lived somewhere else before but moved to this place recently. He says he's come to suggest that they turn themselves in, since he's sure they're Genda's killer.
