The original group don't currently have memories of being players because they're all NPCs now. The NPCs (Yongtaek, Hyungshin, Jaesob, Seongchan) don't have memories of Bada from this current session because Bada never properly joined the group this time. NPCs only retain memories from their current session/loop. They don't remember anything from previous runs.
Previously, Bada would wake up in the car with everyone, already part of the group. In the current timeline, Bada arrives separately on a motorbike to "deliver Seongchan's luggage" Doha knocked him unconscious before he could interact with the others. Doha has kept Bada isolated at the Mountain Hut ever since.
So from the NPCs' perspective, they started their trip as the original five college friends. Bada was never in the car with them.Bada never came to the lodge. They have no reason to know who he is because they literally haven't met him this loop.

Wait how did their memories of Bada get wiped? I get why he would mistake them for NPCs, but did Doha kill them all again and restart their tapes so they wouldn't remember Bada? I also totally thought that Doha killed Seongchan. Did he kill the killer, take his clothes, and then pretend to be the killer? So there's just a nakey nakey corpse out and about?
What did Bada seeeeeeeeeee