That's a poor way of trying to weasel out of the actual definition of monopoly, which is defined as "a company or group having exclusive control over a commodity or service"[0].
What you're describing is a substitute good. When the "choice" is to not purchase said product/service and look to alternatives, you're literally describing the effect of a monopoly.
I'm not trying to weasel out of anything. Of course they're monopolies.
My point is simply that a monopoly isn't some sort of God-emperor who can do anything without consequence. Even monopolies have to bow to customer pressure, they're just less sensitive to it than companies in more competitive industries. Supply and demand applies to monopolies, too, that's why their prices might be higher than they would be in a competitive environment, but their prices aren't infinite. "Going without" is always a choice, even if there are no competitors.
What you're describing is a substitute good. When the "choice" is to not purchase said product/service and look to alternatives, you're literally describing the effect of a monopoly.
[0] http://www.dictionary.com/browse/monopoly