China has already de-facto banned those games for public consumption (by making an ID and 21+ requirement for any game that isn't full-banned, and a LOT of games are full-banned), so banning their streaming is a natural flow of events.

You overestimate the value of China's cultural impact. China wants more Chinese people being born. America does not want more American people being born. There's a strict split in values and desires. And so this will likely not become global standards, as it would lead to an increase in American birth rates, instead of importing foreign workers to make up the shortfall.