Although China is discussed at length in Chapter 16, the answer to this is best found in the Epilogue. It is seen most clearly beginning on page 413 in the paperback edition of the book. There, Diamond says that China lost its lead as a world power because of its unity and Europe became powerful because of its disunity.
These different outcomes arose, as so many things do in this book, from geography. China was united because it lacked an indented coastline, islands, and major mountain ranges. In addition, it had long, east-west rivers. These things made it harder for China to fragment into small political entities.
By contrast, Europe has many peninsulas, some big islands, and mountain ranges. These serve to split it up into areas where distinct ethnic groups and small countries can arise.
Thus, geography ended up causing China to be united and Europe to be disunited.