No doubt the government does have a stake in promoting online games. But is the stake TO SPREAD TEH COMMUNIST PROPAGANDA? I doubt it. As have already been said, China is not Communist. It is a capitalist dictatorship.
More likely, the Chinese government is getting involved for two reasons: 1) to take control of the market boom by bringing Chinese games in line with Western ones in terms of competitiveness and 2) to promote the unity of Chinese cultural norms, as this article mentions:
http://www.dfcint.com/game_article/aug05article.html
Understand that the Chinese social elites have always been a very proud and thus isolationist group. They, like most Asian countries (Korea, Japan, Vietnam, etc.) before the age of imperialism, prided themselves on the superiority of their culture to the barbarism of the outside world. This concept is by its very definition Chinese: a civilization of scholars/philosophers and peaceful peasants surrounded by barbaric, warring hordes (ie the Empire vs. the Mongol Hordes, a classic ancient Chinese image). In modern times, China like most Asian countries have had to adopt a new, more open economic policy in order to compete with the rest of the world. This they did, but not without that earlier cultural ideal. Even now, China is determined to foster nationalism through the pervasive ideology that China's culture must remain "Chinese."
Which consequently is simply another way of saying that China's government wants more "Chinese-style" games. In a continent as fanatic about gaming as Asia, this is akin to defining the pop culture of the future - something that the government undoubtedly wants to have a hand in, having failed already in preventing Japanese dominance in the comic/anime arena. I've no doubt that said Chinese companies are not like the average Western development house in terms of their cultural sensibilities, and that if all of this works out, they'll introduce to the world a kind of distinctly Chinese games (though again, it's likely going to include a mish-mash of influences already present in China via the West & Japan).