Free markets do work well, when such a thing (or something close to it) exists. The problem with the companies in the article is that there's no free market there, these are monopolies or oligopolies.
Comcast: monopoly or oligopoly. In many places, Comcast is the only ISP and/or cableco in town. In others, there's precisely one competitor (usually Verizon). A duopoly is not a free market.
Facebook: monopoly. You can't get an account on some other side and interoperate with Facebook and see your friend's FB posts, because FB is a close, centralized, proprietary platform.
Twitter: monopoly, just like Facebook.
Korean telecoms: I don't know exactly, but if they're telecoms, they're likely oligopolies or monopolies just like the telecoms here in the US.
This is a perfect illustration of why monopolies and oligopolies are a very bad thing, and should be heavily regulated by the government (or broken up if possible). Unfortunately, utilities naturally lend themselves to being monopolies, and having regional monopolies isn't really any better than having a nationwide monopoly since any given consumer still only has one choice, so breaking up such companies usually isn't helpful. So again, what's needed here is a heavy dose of regulation, or maybe even nationalization or competition in the form of municipal (local government-provided) services, such as the municipal ISP in Chattanooga.