No, its not.
> What copyright actually is is a limited-time monopoly right.
Limited time monopoly rights are property rights. A life tenancy in real property is a property right.
(Copyright lacks what some consider essetmbtial features of ownership of the subject matter of a property right, as opposed to ownership of a property right in that subject matter, but ownership of the subject of property rights is not the only kind of property right.)
Copyright may be owned, bought, sold, transferred or otherwise discharged in the same manner that any other form of property is. Nothing about property inherently implies such claim exists in perpetuity.
I was interpreting "property right" at a different level of abstraction than you. I was thinking it was referring to the thing that is copyrighted as being the "property", not the copyright itself.
Changing my frame of reference up a level of abstraction puts us in agreement, I think.
In many ways it resembles a property right, but it is missing fundamental aspects of property rights.
What copyright actually is is a limited-time monopoly right. When it expires, the creator of the work loses that "right". It exists not for the benefit of the creators of a work, but for the benefit of the public.
Copyright is a temporary restriction on the rights of others. As a society, we deem that acceptable because it's temporary and because it encourages people to make their works publicly available, thus enriching culture and society.
If it were a property right, then it would make no sense that you lose that property at the expiration of copyright.