Would be neater if the game generated a new script procedurally each time
You'd procgen the mysterious bit, and then the stream could display the game seed on the screen or in the title, so players could go to the game's website and access the supplementary material for that particular game.
That's basically what I was suggesting; "mysterious bit" would refer, in the archaeology game, to the hieroglyphs.
The supplementary material shouldn't just be a decipherment key for the hieroglyphs, but something like a full catalogue of artifacts from that culture (some of which have writing on them and/or accompanying text from past archaeologists), generated from the seed that the game generated. That way the viewers have something that stays still for a bit, so they can puzzle things out in peace without being completely dependent on the streamer's POV.