My guess is he wasn't the first kill like Bada had thought he was. Bada at this point in the story the author has made clear is an unreliable narrator since he is too confident in what he thinks he knows. So he gets very tunnel-visioned and only notices things he's purposely looking for. So my guess is the cousin always faked the same beginning script for Bada because he knows Bada thinks he's the only "playable" character. And he picked a phone call to have an easy way to keep Bada unaware but to also let him get away from everybody else so he could truly play and with Bada being shown as the unreliable narrator he is, I bet he had probably just always thought that the cousin had been the first kill since he never came back (and he thought the cousin was an NPC with the same character program every game meant to serve a purpose aka the first kill) so he never actually confirmed it in any game since he felt confident in it. We as the readers just thought he was always the first kill because we were following what Bada had been saying, but the author is showing us in these newest chapters that we can't trust something just because Bada had been confident in his own thoughts.
So the cousin knew what was going on but choose to die repeatedly???