Obviously we are approaching this in the context of different frameworks with different definitions of property. IMHO attempting to define property as a right to prohibit others from deriving any benefit from the good—regardless of whether their actions affect your own use of the good—is self-contradictory, contrary to human nature, and a source of needless conflict. Scarcity is the obstacle here, and property is how that obstacle is addressed. If there is no scarcity then there is simply no point in attempting to allocate property rights—you're taking something superabundant and making it scarce for no net benefit.

Even if you do stretch the definition of property to include copyrights and patents, however, the fact remains that these are non-rivalrous goods, which implies that you are not harmed when someone else ignores your claim to exclusivity. No response involving force (including fines, imprisonment, etc.) could ever be proportional to the supposed offense, which means this is a "right" you cannot justly enforce.

Exclusivity, and the ability to justly enforce it, are common characteristics of property exactly because most of the things people try to classify as property are scarce and rivalrous. You can try to extend the definition to include things which are neither scarce nor rivalrous, but if you do so then the justification for enforcing property rights no longer applies to all such "property". At that point you've accomplished little beyond turning the word "property" into a useless label that could be applied to almost anything and which does not imply anything about the rights of the property owner.