China today resembles the Bush era in America: Hard-liners are ascendant. Brace yourself.
The key to your question:
However, in this particular case, what does 'Brace yourself' mean? Is the author casting this word to Chinese, or Americans?
lies in these portions of the article (emphases mine):
My take is that China is going through a period resembling the Bush era in the United States: hawks and hard-liners have gained ground in domestic politics, and they scoff at the country’s diplomats as wimps. China’s foreign ministry seems barely a player.
The upshot is that China-Firsters — Chinese versions of Dick Cheney — have a greater voice. Brace yourself.
Kristof's point is that regardless of whatever goodwill China's leaders in contact with the outside world (president, prime minister, diplomats, etc.) try to garner, powerful domestic elements (hawks, hard-liners, Cheneys, etc.) are at play behind the scenes and the significant influence they wield within China will have external ripple effects.
Indeed, the subject of Kristof's final sentence, "Brace yourself", could be ambiguous. On the one hand, one could argue that he is referring to Americans, in general, warning them to get ready for the onslaught of the Chinese Cheneys who are gaining strength with each passing day. On the other hand, the subject of the sentence could be the reader of the article, whoever the reader is. (I favor this line of thought.) Thus, whether you are Chinese, American, Brazilian, etc., well, brace yourself, anyway, for the impact of the China-Firsters on whatever corner of the globe you inhabit.
Brace yourself can also be read as steel yourself (although steel yourself is not as idiomatic an expression). Here are the relevant definitions:
Another related phrase is brace up:
You know you are bracing yourself whenever you do any of the following:
- arch your back
- breathe in and out slowly and deeply
- clasp your hands
- close your eyes
- crack your knuckles and steel your nerves
- grab a hold of your body or nearby object
- hold another hand tightly
- make a low whistling sound
- make your posture erect
- tighten your face into a grimace
- tighten your fist
- tighten your jaw
- say, "OK, let's do this!"
- stiffen your neck
- wrinkle your forehead, etc.
One example, for brevity's sake:
We're going down, mate. Brace yourself for the impact!
Also, I would recommend that you consult Merriam-Webster Online whenever you need to find the meaning of a word or phrase, especially in American usage. Urban Dictionary is great for streetwise lingo, slang, colloquialisms and newly-coined terms, but it is not a standard dictionary, in that its content is user-generated.