As an attorney who specialized in IP practice in law school, I can tell you that your understanding of what a property right is is absolutely wrong. If you told a judge that copyright is not a property right, they’d stifle a laugh and advise you to come back with a lawyer, and your lawyer would, in turn, advise you to keep your legal opinions to yourself.
Both are rights to exclude enforced in law, which is the essence of what property law is. As the owner of physical property, you can exclude others from occupying or using it (with the violation being trespass). As the owner of intellectual property, you can exclude others from copying it, making derivative works, etc (with violations also enforceable in law).
Yes, both types of property rights are subject to limitations, either by law or by contract (as in the easement and mineral rights examples you gave). But that doesn't change the essence of what they are.
Legal definitions are often not the same as plain English, and wording used in legislation is often politicised.
The nature of copyright is that it is a monopoly right. It is almost indistinguishable from letters patent (e.g. in the case of the KJV Bible in the UK). I am less familiar with US law but I believe US copyright law is based on a clause in the constitution giving the federal government the power to grant monopolies?
A monopoly right and a property right are the same thing with different names. As a landowner, for example, you have the right to kick people off (evict from) your property. You have both a de facto and de jure monopoly to exploit your land.
The US constitution confers to Congress the power to grant copyrights and patents in Article I, Section 8:
"The Congress shall have Power ... To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries"
The operating word here is "exclusive" which, yes, is a monopoly right. But again, it's not different in essence from a property right, which is also a monopoly right.
Both are rights to exclude enforced in law, which is the essence of what property law is. As the owner of physical property, you can exclude others from occupying or using it (with the violation being trespass). As the owner of intellectual property, you can exclude others from copying it, making derivative works, etc (with violations also enforceable in law).
Yes, both types of property rights are subject to limitations, either by law or by contract (as in the easement and mineral rights examples you gave). But that doesn't change the essence of what they are.