The author's misuse is all the more painful for being an econ grad student at my alma mater, GMU. A former professor of mine, Russ Roberts (the man behind the Hayek vs. Keynes Rap video), even used a similar example ("Does Ford have a monopoly over the Taurus? Cars? Means of transportation?") to show how little objective utility the term “monopoly” holds. The more narrowly one defines the market, the more one is likely to “discover” monopolies.
Don't forget though, Russ Roberts has an ideological dog in this hunt, and he'd like to recruit more anti-regulation followers, so he'll bend the argument to suit his biases. There is a sorities paradox element to it, but that doesn't mean "pile" is undefined; Ford has a government-granted monopoly - a trademark - on Taurus.
That substitutability is defined in a distributed way isn't a well-formed argument against tying it down in any particular case. Legal courts make these determinations every day concerning the meanings of texts, whose intent can be similarly hard to divine.
We should all have a legal monopoly on who we are. Protection from others pretending to be us. That's all a trademark is. Its not at all like a government granted monopoly that enables a company to be the sole provider of phone or automobiles.
Which we generally call a patent - in my understaning the only real monopolies are government granted ones - i.e you must use ATT for phones, or no one else can manufacture widget X
Maybe this explanation will help you see how your response to the parent just goes to prove his point:
"Monopolies are thus characterised by a lack of economic competition for the good or service that they provide and a lack of viable substitute goods." - via wikipedia, with book citation: http://en.wikipedia.org/wiki/Monopoly
Please don't forget about the last bit. There are a million (bad) substitutes for an iPod, regardless of how they end up connected to the computer. The word monopoly should be used with economic rigor or not at all - even economists tread lightly and discuss heavily before labeling any entity a monopoly.
I actually dislike the wikipedia definition. It suffers from the same general definitional problem: which market?
Setting aside the above, the definition suffers for ignoring the question of why there are no viable substitutes. It's a dangerous omission since the implication, at least with respect to legal policy, is that it is the "fault" of the firm.
The closest one could get to a useful definition of monopoly would be: a firm whose would-be competitors are coercively excluded from competing in the market. Of course even that still suffers from the subjectivity of defining the scope of "the market".
That being said, the term monopoly doesn't mean much on its own. There is an alternative to everything.