Monopolies wouldn't exist or form with perfect competition (in theory, monopolies would be overcome by an infinite number of startups undercutting them), but there is no such thing in reality and monopolies have so much market power they can just buy out or undercut startups indefinitely. Also borne out by reality, where the vast majority of the time monopolies must be dismantled by the state. It's a little tricky in that the government also allows some companies advantages over smaller companies, but in general a government is much more dangerous to a (non-state) monopoly than it is beneficial. Anywhere you get weak governments, you immediately get markets that are entirely dominated by one company or group, who then usually manipulate prices and quash competition.
More generally the idea of laissez faire economics/libertarianism is that government actions are "unfair", and that causes the problems. In reality if there are "unfair" actions, they are far better used by the government (which normally has the interest of its citizens in mind) than they could be used by corporations (who have the interest of their shareholders in mind). NB that this is a strawman attack and that some types of libertarian philosophy knowledge some kinds of rules and government are necessary, but that kind of reasoning is not at issue.
What the quote says is that 'getting the government of your back' reflects the infatuation with 'Mussolini's fascism's corporatism'. He is not equivocating. He's just saying they reflect the same thinking.
First of all, most obviously, Mussolini's fascism is the destruction of the people's government, and its replacement with corporations. The only difference is that the corporations are constructed by the government. The reflection comes in the lack of a people's government so that corporations or market forces decide what the people do. In that way, pure libertarianism and Italian fascism are superficially the same. It's not hyperbolic, its a real parallel, similar to how you can draw a parallel between communism and dictatorships through (varying amounts of) authoritarianism. Fascism and libertarianism are parallel due to having no (or lesser) personal representation.
Unrelated, but following from that, is the idea that the government is basically a union for the people. Individually a person has no recourse against a greater power eg a company can fire me on a whim, and it may easily ruin my life but will certainly be a large upset and setback as I lose 100% of my income. Meanwhile that company operates at 99% efficiency for a few weeks or months, before returning to 100%. The company is clearly less bothered by firing people than they are. This stance rejects any idea that the government is less than (or at least, that it should be less than) operated to further the interests of its citizens. It rejects Hobbes. Under that, "getting the government off your back" is perverse- it means unloading your ability to advocate for yourself onto a despotic party who is only interested in their own goals, be it money or the "state". Fascism does this overtly- its literal intention is to remove all power from the individual, and give it to the interests of the state. Libertarianism does it obliquely, but nevertheless if you assume the government should represent the people's interests as a whole, then it can only be taking away power (power derived equally from everyone, implying democratically) and giving it to someone else. That makes it much easier for corporations to force individuals into making poor choices because again a corporation by its nature has better information and more resources than individuals, and can always get the upper hand.