Not really, not without an extremely narrow definition of what market they occupy.

The "daily deals" model is only one of many ways for businesses to offer deals and try to find new customers, and for customers to find discounts. Groupon/LivingSocial/etc have many competitors, all the way down to simply advertising specials and promotions with a sign in the window.

A monopoly on “an industry that doesn’t really exist” - citing the article.

In the same sense that YCombinator has a monopoly on news forums run by startup incubators.