Earlier quoted context omitted.
Depends on how you define monopoly. The analysis is intended to cover any business that faces a downward sloping demand curve. That is, any one who is not a price-taker. A monopoly certainly does.
> The analysis is intended to cover any business that faces a downward sloping demand curve. That is, any one who is not a price-taker. Those are two different things. The vast majority of demand curves are downward sloping. (The exception being products which show strong network effects.) The key thing about a monopoly is that it is a price-setter, not a price-taker.
In reality, as you point out, each firm has at least some pricing power, for various reasons, and so from a theoretical perspective they are a monopolist in some good or service defined in the right way. However, In common and legal usage they are not a monopolist.