There's going to be several factors here...
Beating America at science education is like beating it at cricket, it's just not what America does. It's a nation where 40% of the population don't even believe in evolution.
As Andy says, migration is acting as a Heinlein filter.
Ironically that also boosts American figures, since it has enough immigrant kids to partly compensate for the utterly wretched state of science education.
It has reached the level that in The Simpsons a teacher can remark that her school results are remarkably good considering they have no Asian kids. When you are at that point, there is no way back.
China has almost no lawyers, but for many bright Americans this is an entirely rational choice, which means that people who might have done science choose liberal arts.
US manufacturing is of course doomed, any American smart enough to make a difference to this avoids even trying, and so it's not clear to me why a smart kid in the US should choose to pursue science. And yes you have to persuade them since the media is more hostile to scientists than it is to Nazis. At least some Nazis look cool and powerful, occasionally attractive, no scientist like that ever appears on US TV.
In China, a smart engineer / scientist kid can look forward to a job that pays more than his parents put together, and in many cases earning more than his whole village is a feasible goal. That means Chinese kids want to be scientists or engineers, and there is no peer pressure against studying science. That is very unlike the USA
A few caveats...the tests are in the People's Republic of China and I would not entirely believe the result of any education test that took place there, even if I monitored it personally. Note they said "no evidence of cheating". This is China of course there was no evidence. Given a choice between believing that the whole city of Shanghai does not actually exist, and that a Chinese exam was free of cheating, I'd be wondering if Google Earth could be hacked.
Many Chinese don't get the same education as in Shanghai, and although it is bad for them as individuals, for the PRC as a power, that doesn't really matter. If you produce far more excellent scientists and engineers than anyone else, you will succeed, and losing a few hundred million people makes little difference.
