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.
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