The article doesn't make this clear, but 关系 in Chinese is a very general word that can refer to any kind of relations/connections, not only between people but between institutions, abstract ideas, etc.
No. Mind you, the USA government/uniparty is corrupt AF. Most businesses in the USA have all kinds of corrupt practices, especially bigger ones. But by your statement it appears you have no idea how prevalent guanxi is in the very fabric of Chinese society. In the states an unknown person with a good idea can still get ahead without it, but in China that's just not going to happen. Problems range from permits being slow-walked or magically made up on the spot, to bribing all kinds of local party members, to SWAT-style morning wake-ups, to having your relatives punished for your not going along to get along.
We have this in the West, as I understand it at least.
Move to another country, and you will notice the absence of a network that you took for granted. It takes years to rebuild it.
If you go through something for the first time, you can call upon the experience and recommendations of other people in your network. As an immigrant you really start from scratch and a lot of people don't think about that challenge before they move.