I can't see that the expression "oral transmission" needs to be taken as excluding recorded performances, or pen and paper or print or computer screens, as part of the chain. People can learn a song from anywhere - what matters is what happens next as they sing it and pass it on. That's where "the process of oral transmission" come in.

Still seems a pretty good definition to me. 1954? What's fifty or so years, after all?

I think about the only thing I'd alter would be that in "The term does not cover composed popular music that has been taken over ready-made by a community and remains unchanged" I'd remove the word "popular".