I'd argue that China has achieved superpower status at this point. But I agree with you that there could be a third world war without the US, just like last time. However, it'd be difficult to have such a war without a superpower. Last time, we had a few more of those.
I think the PRC lacks something in the soft power stakes; they've created some degree of good will outside the West, but they suck at projecting cultural output that doesn't stem from the imperial Chinese era.