Does starvation freedom imply progress?
It depends on how exactly you define "starvation freedom" and "liveness."

I believe the book is talking about starvation freedom from the perspective of the OS scheduler, which usually does not know about locks managed by user processes.  So, the book is partially right (in some context).

Your definition is more broad and is what someone working in distributed systems would think (see https://en.wikipedia.org/wiki/Liveness.  Note the important assumption "All processes are assumed to correctly use the mutex...").

However, I'd think that "liveness implies starvation freedom," but there's no justification in the book for the first statement in the answer.