The telephone game lacks features in the telling that are common in oral storytelling that help reinforce the content and reduces the number of errors. Repeated telling, repetition in the structure, rhyming and alliteration (which is used, or even if they're used, depends on the language), being made into a song (seems to stick better than just straight speaking), etc. If you played the telephone game with a deliberately constructed story using those elements and taught that story to the next "generation" by repetition over a period of time before they, in turn, repeated it to the next generation it would be much more reliable. It also wouldn't be the telephone game.

I'm convinced that poems are an effective error-correcting code for remembering things.