Short form (AKA: Seven words for you): Gavin Menzies is not a credible historian.
Long form:
Zheng He can presumably make such a voyage, though not easily (it is a very long trip). But it is well beyond any reasonable distance China can project force on a regular basis, and without being able to do that you have some Chinese introduced butterflies and viruses at most. Not Chinese rule of Europe.
Even rule in the sense of overshadowing Europe.
Now, for China to be so much more powerful and dominant that the kings of Europe are irrelevant on the world stage for some time is easy. That's what happened OTL, no reason for it not to happen here. But that's considerably less than China "dominating" the kingdoms of Europe or being a "world empire" in this period (up to and including the equivalent of the 19th century, specifically meaning steamships and the telegraph).
Considering the Mongols conquered China as well as Eastern Europe you do have a potential analogy there, but this was several hundred years later and required a mass army across the whole of Asia - something one does not see traditional China doing
That only leaves 2 options - one of which is naval power, which seems one hell of a push unless someone builds the Suez Canal early (didn't the Romans try?), the other of which is mercantile power, trading colonies and associated armed merchantmen which might JUST work in being an extension of Chinese power and influence, but still seems to fall short of the idea of getting the European kingdoms to acknowledge Chinese suzerainty - except where doing so might be in the short term political interest of a passing ruler
Best Regards
Grey Wolf