I trust the authors immensely but i don't see what yet another class system in R solves. That's on me, but I'd like to understand more of what motivates this effort.
It then goes on to describe what that means in depth.
It describes 3 new generics in base R that help their new S7 system.
It all seems motivated by better interop with python which is 'neat' but really doesn't seem like a critical necessity of the language. I guess it's more of a tactical thing where they're trying to make it easier for python users to eventually try R. Or for R users that work alongside python users to not abandon R.
If you're interested in what motivated S7, you may enjoy this talk Hadley gave: https://www.youtube.com/watch?v=P3FxCvSueag (R7 was the working name for the package at the time)