Exclusive rights and monopolies are not the same thing. Monopolies are about access to a category of things or services that fulfill a need, not one specific thing. E.g. Samsung has exclusive rights to sell Samsung TVs, but they don't have a monopoly on TVs, and talking about a monopoly on Samsung TVs specifically makes no sense. Similarly no one has a monopoly on landscape drawings, rock music or scifi movies, just exclusive rights to specific pieces of art or literature that they created.

As a side note, patents are a different story imo. Because overly broad patents can actually give you exclusive access to an entire category, and therefore a real monopoly. But you can't patent art.