If you take the above definition too literally it sounds more socialist than capitalist, and I think it accurately defines the Chinese government today.

In the USA the government doses the economy, more or less depending on who is in power, but Wall Street and other stock exchanges represent a free market. Supply and demand is often manipulated but in the end it is a more or less a controlled/limited free market.

The IC is not a government controlling the economy, but rather a corporation acting as a government.  Considering that a corporations priority is simply to make profits, that would be about the worst thing that could happen to a country...or planet.

I doubt that it's really one single company, tbh. The main way that the Iridium Corporation could become such a vast, galaxy-spanning organization is going to have been through mergers and acquisitions. If there's no barrier to entering the market, then it's still a free market - the Corp probably just buys out the best examples of any of the small-fry businesses that crop up with each new generation of technologies. Combine that with a truly enormous amount of sub-division within the company (it's subsidiary structure must be truly insane), and it's entirely possible to have a large number of competing subsidiaries operating in a free market, but all effectively owned by the state.

Think about Silicon Valley. Silicon Valley is basically a bunch of vastly powerful monopolies. Microsoft absolutely dominate enterprise software, even though there's free alternatives to all their software. Google completely owns advertising and search to the point where their advertizing platform basically demands to be allowed to rape your wallet at will. Facebook controls social media; VMWare reigns supreme in enterprise virtualization tech; Netapp basically IS the network storage hardware market; Amazon is the undisputed master of online shopping. Yet innovation continues, because the reward for entrepreneurs is being bought out by one of these established monopoly players - usually for billions, and usually within 4-5 years of starting up. The profit motive is actually accentuated, because the amount of work needed to achieve enormous rewards is lower than it would be in a less monopolistic sector.

Anyway, there's not really any reason why a state-owned company can't compete in a free market - the problem is largely a matter of governments choosing to bail them out when they're unsuccessful rather than letting them go bust. Presumably, the Corp has no such compunction, and happily allows unprofitable subsidiaries to go bankrupt.