For games I believe American companies cannot directly sell their product in China, they need to go through a Chinese company. Blizzard went through Netease, Valve goes through Perfect World, and Riot is 100% owned by Tencent anyway.
When China first started allowing western movies in, they required the movies be censored for Chinese audiences.
Then that wasn't enough and movies had to be censored to western audiences or they wouldn't be considered and in fact anyone connected to an anti-China movie would be blackballed (look what happened to people involved in Seven Years in Tibet).
Now movies are required to push the CCP party line in the west if they're going to be considered for distribution in China.