Your argument against "nonrival" would imply that if a manufacturer creates surplus product, its ok to steal the surplus because no one else needa it.. even if they go bankrupt because no one then buys the non surplus.
And a Marxist would say that labor ia property, and its rheft to deprive a laborer of ownership of their labor. All property is a legal fiction, you cant arbitrarily decide that one kind ia legitimate and the others aren't. Rivalry is just one factor.
I may side with the Native Americans on that one.
There is this idea of a Land Value Tax, where most or all taxes would be taken on naked soil. Such a tax would effectively abolish land ownership, because everyone would effectively rent it from the state. Long story short, it looks like it might work.
Do not dismiss him too quickly.
By the way, the concept of IP is obviously dysfunctional: ideas and expressions are non rival goods. They are not moved, borrowed, nor stolen; they are only copied from substrate to substrate (be it a mind, a piece of paper, or a computer). Property rules simply don't work there.
What does work is monopoly rules, such as copyright, patents, and trademarks. The use of "property" to describe such limited state granted monopolies is an obvious piece of newspeak, an Orwellian ploy to make those laws look better than they are, and frame the discussion: if you're against monopoly, you're a normal person. If you're against property, you must be a thief of sorts.