I basically agree with Steve’s interpretation (by the way, I’d written a long response to this question a week or more ago and apparently never hit “submit,” uggh).
I think Peikoff could have been clearer, but I take him to be saying that men in what’s traditionally called a “state of nature” will not yet have grasped the concept of rights or the various ways in which they apply. It’s not that rights wouldn’t apply but that people don’t yet know what rights are, so they aren’t in a position to know how they apply.