Earlier quoted context omitted.
The irreducible state role in a free market is to enforce property rights. Almost all free market fans I have seen think that this should extend to some notion of intellectual property.
I think the standard answer to your point is that you can recognise "intellectual property" without granting a (limited) monopoly. There are plenty of proposals floating around for copyright and patent reform that curtail or replace the ability of the creator/owner to unilaterally set the price and decide who can license the material and how they can use it.
I also think critizising intellectual property on grounds of granting a monopoly is muddling the language. If I write a novel I have exclusive rights to the novel. But I am not the only supplier of mediocre novels. I don't have a monopoly in a relevant market.
None of this contradicts the point that IP and patent rights are in desperate need of reform, or that they can play a central role in abusing a monopoly position (e.g. https://en.wikipedia.org/wiki/Orange-Book-Standard).
Edit: Maybe my post was unclear: I would agree that IP should be abolished. But this is not a position I have seen classical market liberals and other free market advocates take. Instead, they tend to favor strengthening all forms of property rights. If I am wrong on this point, I'd be happy to read some examples.