OK, see, this isn't "cornering" rare earths...
The Chinese have no need to monopolize a resource they've already got a lock on (at current prices) - this is an attempt at using their existing (effective) rare earth monopoly to create better-paid, skills-intensive jobs in high-tech manufacturing rather than getting stuck with the low-added-value stuff (like, uh, mining) while other guys do the really profitable jobs.
This strategy of forcing your foreign clients to buy finished products instead of cheap raw material near the bottom of the industrial chain isn't exactly exclusive to the Chinese, either - Japan does it for such relatively pedestrian stuff as fancy steels.
Will the strategy work?
Maybe. As the author pointed out, people in other countries could start mining the stuff if the price made it worth their while; on the other hand, the Chinese could ensure they'd remain the most competitive by simply not raising the price of the raw stuff and providing a labor pool at significantly lower cost than your Western worker. Which, you know, is what they're famous for.
The only things I can think of that would make this not work would be if a) capital costs for setting up a new factory in China outweighed the benefits or b) our lords and masters got around to slapping a reasonable import duty on Chinese products.
(By the way, (b) just isn't going to happen, boys and girls).
The author is also right that we don't know how tech is going to evolve. Rare-earth stuff could be completely obsolete five years down the line - or the stuff could be 10 times more valuable as new products that use it evolve. What won't change is that highly-skilled jobs will be more valuable than low-skilled jobs, and the Chinese are doing their best to ensure they get their fair share of the skilled ones. I just wish we could say the same.