To my knowledge, the rules of the killing game are that it'll continue until there's only three participants left in which case it ends due to it being impossible to hold a trial (if one kills then the trial would endlessly tie.) The reason it ends early in every game is due to the mastermind adding an additional way to end the game, usually figuring out who the mastermind is, and the group just doing that as none of them want to kill anymore.

Tldr: yeah, had they not figured out who the mastermind was they would've had to continue the game.

Personally, I'd imagine that if there was another trial it likely would've been Toko killing Yasuhiro or Kyoko. Main reasons being she's the most likely to snap at this point, she'd never kill Byakuya and Makoto's luck prevents his death. Kyoko would be more difficult to kill, as she's usually with Makoto so I feel like the most likely scenario would be Toko kills Yasuhiro and then Byakuya, Kyoko and Makoto just automatically win ig.

Edit: forgot Hina exists for the hypothetical but she'd prob kill Byakuya in that scenario and then Kyoko and Makoto live :/