FWIW, I can attest to 'music as a language' experience - in two different conversational modes.
First is the obvious one: Where the entities conversing is the music and myself. I think most people can relate to this unidirectional experience.
Second, and less observed mode, is when consuming mostly-instrumental type of music. Here the entities 'conversing' have to be inferred, but most often my mind will settle on giving each instrument a personality.
In this mode, I'm merely a bystander listening in on a conversation. I often automatically imagine these instruments talking to each other, and the act of listening is simply an act of interpreting what they are talking.
This would be nothing new to many people reading this, but I know many people who often don't listen to music. Check this short clip if you want to play with this: https://www.youtube.com/watch?v=Tf-QV8Z8Pww