This is actually one of those cases where the dictionary definition isn't really helpful or applicable. Because that definition is based on a literal meaning of the word and not the actual economic implications. Economically speaking once a market is dominated to the point where you cannot compete economically that is what we call an effective monopoly or actual monopoly. Basically a real life monopoly.

Think back to when Bell was broken up. It wasn't the only, exclusive, competitor in the market. However they owned such a massive market share that they had to be broken up because no one could effectively compete. You'll see how using the literal and ineffective definition of monopoly would be extremely easy to defeat for companies exercising actual monopolies.

So basically the other guy is right, albeit expressing himself rather dickishly.