Menzies' thesis won't die. Just when it seemed to be fading out (unless Menzies' argument about Mongol exploration is really his next focus), along comes this map (discussed in more depth here; update: and with translations of the notations here, and much more discussion by actual map historians here) which claims to be a 1763 copy of a 1418 map of the world. The Economist story even cites it as a possible source for previously unexplained pre-Columbian maps showing (something vaguely resembling) the Americas!
The map is an 18th century copy of a European map, as evidenced by the two hemispheres depicted, the continents shown and the non-maritime detailed depicted. It proves nothing other than the Chinese (and Japanese) were copying European maps. That your writer has contributed to the Menzies' bandwagon and its continuing deception of the public is saddening. The support mentioned all comes from Mr Menzies' band of acolytes and the claims have no academic support whatsoever.
He goes into some detail on both the maps and "experts" cited, and I'm sure H-Asia will be abuzz for a while on this topic.
There are two things that I find interesting about this, on first look.
First is that it would be an interesting exercise actually tracing the intellectual and cartographic lineage of this map. I don't know much about cartography (is there a cartographic equivalent to "historiography" for writing about the history of maps?) but a map of this quality, if it existed in the 15th century, would have spawned imitations and copies pretty quickly. Contrawise, the number of European maps given to Chinese, Japanese or Korean mapmakers in the 18th century for copying must be a fairly finite number, and European mapmaking seems to be a pretty well-developed historical field: if it's a 1763 copy of a more recent imported map, that should be something which might be traceable.
The second thing is that the direction in which you study this map depends a great deal, clearly, on what you already believe about this map. The articles cite claims that such a map could have been constructed in 15th century China but, as we historians know, that which is logical, possible or even plausible "ain't necessarily so," because history is not about logic. It's about what happened. That cuts both ways, of course: I think Menzies' thesis is bunk; most historians of China that I know of think it's bunk; the evidence that we have against the thesis is much stronger than that which has been offered in support of it. But, just because it doesn't make sense to us that the Chinese would visit the Americas and leave almost no trace in their own historical record doesn't necessarily mean that it didn't happen. It means that the evidence in favor of Menzies needs to be more than just suggestive; it needs to be clear, verifiable and reliable. This means that it can't just be one piece of evidence.
I was actually just having this discussion with my World History class with regard to the document readings. One piece of evidence in isolation tells us almost nothing. It's the accumulation and cross-referencing of evidence which actually allows us to critically and reliably read and cite documents. A map copy like the one cited here could be considered authentic if it came from a copyist known to have access to lots of old maps, if it bore traces of information which we could verify as being extant in the early 15th century, if it left behind its own imprint on later intervening maps (whose creators might credibly have had access to this one), if there were descriptions of world geography in China which resembled this image, etc. Absent those supporting materials, a map -- or any other piece of evidence -- is simply a single data point. As my father says, given only one data point, you can draw any line you want to....
Menzies' supporters and believers will claim that the map is one more piece of evidence for his thesis; his detractors like myself, who find the evidence he's already cited to be highly suspect, will continue to point out that this map is not, in itself, clear evidence of anything, though it does suggest avenues of investigation.