Personally, I still don't see China as a superpower, not yet, probably in about 7-10 years they'll be one with us, but at this moment, they're still trailing a ways behind.
Here's a definition of Superpower I like to follow; "A superpower is a state with a dominant position in the international system which has the ability to influence events and its own interests and project power on a worldwide scale to protect those interests."
Three points highlighted.
1. China is in a Dominant position. By the loose wording of "International system:, that includes mostly the Economic system and the UN, China is a permanent member of the Security Council and China is the manufacturer for most commercial items, so thus, they are quite dominant there.
2. This means of China's political power, which is derived from their Military power. I'll cover why China does not meet this requirement below.
3. Projecting power on a global scale, is conventionally done with a Navy. Sure, an ICBM can go anywhere, but it's very hard to show people your brand new Dong Feng. However, something along the lines of a "Great White Fleet" will project power anywhere in the world, as long as that fleet can get there. China does not have a Great White Fleet. The PLAN is focused mainly on it's traditional task (and historical one) of protecting the Chinese shores from Foreign attack. The PLAN however, does not have the Ships or the Logistics to actually sail a fleet and project power to nations abroad. It fails here.
Influencing events comes with a Fleet. But, you can also influence events by "mentioning your disdain" for something. For example, Barrack Obama can say, "I love Tofu", and he'll give out something called the Opera effect, where Tofu will literally experience a 500% increase in both notice and sales. If Hu Jing Tao said, "I like Hamburgers", sure, that may get some attention, but the local Chinese won't exactly feel more inclined to purchase a hamburger after hearing that. Same goes for larger political situations. If America condemns a country for something, a lot of people will take this as dogma and disagree with that country along with America. China can't do that. So thus, it fails.
One more thing, having a Cultural empire by the means of World Media and Cinema isn't a biproduct of Superpowerism, it's more or less what would be done to draw the world's attention for that Country. For example, the BBC is a World leader in News, yet the U.K. is not a Superpower, a great power, however. Russia Today is a world leader, yet Russia is a great power. Al Jazeera is a world leader, yet Qatar is not a Superpower. List goes on.