I don't know who "we all" is who has the impression that China doesn't have access to the global internet. There must be thousands of people on this website alone who have either lived in China in the past or still do now who regularly comment and show that not to be the case. There are plenty of articles in the mainstream western media that discuss exactly how censorship and surveillance works in the country.
Steam is one of the few popular international services that escaped getting blocked by the Great Firewall, despite hosting content that the Chinese government ostensibly considers illegal or inappropriate. There have been a lot of articles about how Chinese indie game developers were using Steam as a loophole to sell their games without getting the official government approval to sell games inside China. It's never been clear why Steam was an exception to the blocks, but that's par for the course. The government never explains to the people why something gets blocked, sites just suddenly stop working from one day to the next and the people are expected to accept it and move on.
The internet blocks are set up by the internet providers in the country, so somebody must know what's going on, but - like many things that happen in China - the people just need to guess the reasoning by reading between the lines of impenetrable Party literature or relying on supposedly independent editorials in the tabloid newspapers.
So nobody knows for sure, but people have deduced that there are several reasons that the government blocks websites. One is as a "punishment" for a foreign company, because that company published content that insulted or offended some officials in the government. Another is if the foreign company is specifically and deliberately producing content aimed at Chinese-speakers that discusses topics the Chinese government does not want Chinese people to discuss freely (June 4/Tiananmen massacre, Hong Kong autonomy, alternative governing models that do not include the the Party at the core etc). Another one might be if the foreign company refuses to allow the Chinese government to install their surveillance hooks. But I think perhaps more relevant to the case of Steam is economic protectionism - the Chinese government tends to block foreign services that could compete with Chinese companies, so that Chinese companies can become dominant in the space.
The thing with Steam is that there wasn't really a local alternative with a wide enough catalog of games that it would please the middle class/educated/moneyed gamer in the country, so that's probably why Steam was quietly allowed to continue for so long. A few years ago Valve announced a partnership with Perfect World (local media company) to produce a Chinese version of Steam, but for whatever reason it took ages to come out. Now that it is out, and presumably up and running (I don't know since I don't live in China any more), the government has no incentive to allow people to buy from the international version, so that is probably why it now got blocked.
As usual, Chinese government only block in one direction - every day, every month, every year there are more and more things blocked. Eventually even though technically people in China are still able to visit most of the internet outside of China, the sites that are the most popular in China will all be owned by Chinese companies (or partnerships) and exist completely inside the monitoring and self-censorship bubble of the Chinese cultural sphere. So it's not like people in China don't have the opportunity to see other content, it's just that those other sources are very far outside the mainstream and not frequently accessed by the average person. If it did become popular, that's when the government would make a move.