Kazakhstan is ranked 155 out of 180 countries on the World Press Freedom Index, their authoritarian government has nothing to envy from the media in the West.
Although the igniter are energy prices, Kazakhstan is a pseudo-democracy of limited free press and limited free speech, they can even arrest you for practising religion outside of state control, that is why people are so angry, while in Europe or USA people can protest some other way, the chances of doing it peacefully in Kazakhstan are very small.
In what kind of country do you think the government takes down the Internet because of protests? Only in an authoritarian regime like Kazakhstan, it would be unthinkable doing that in the US or EU.
It wasn´t the government who sued, it was the families of the dead children.