Uhh, sure they do. I traveled to Singapore approx 4 years ago. Unprovoked, I probably would guess about once every three days, a topic of politics came up in discussion. (There's a highway which dividers can be moved to the side and roads cleared so that it can be used as a landing strip for fighter jets... etc.)
Taiwan, this May. Lots of mention of competition with Japan, Mainland China, Hong Kong and even Korea. Discussions ranged from Pearls, electronics, tea to food. Taiwanese also love to learn about Western culture but also delve into other Asian cultures as well.
Hong Kong. Many people are quick to begin chatting about other countries to visit. Discussions about Mainland China are frequent as well. Usually it's about the Chinese government attempting to control the Hong Kong government which is a "special state." Oh, should I also mention that my senile grandma talks about world issues in detail? (Not that I really care)
Japan, last year... well, most should know how it works. No need to add. (And since you've confirmed this one as well)
Most of these countries will know of at least 1 or more countries for the following reasons. Economics or politics.
Malaysia and Singapore are at odds with each other. Most of their military power is facing against each other in case of altercations.
China. A bit more closed off, but they're closed off from even their own information at times. I can't say whether Mainland Chinese knows a lot or a little about politics or trade. However, my friends who go on exchange programs say that they like to discuss stuff about other countries, love to show off "borrowed culture" like anime, western songs etc. But since I myself have never been in those places but instead the more "touristy" areas... I personally don't know.
North Korea and South Korea. Need I say more?
Japan. A little more closed off, but one usually does not deny the average Japanese knows a slight bit more about politics or relations with other countries than the Average American. (They might be against other cultures going in, but they know what they don't want in)
Hong Kong. EVERYONE knows in this area. It's because they were under British rule. Not to mention, Hong Kong is considered the world's city or something like that.
Taiwan. Linked greatly with Hong Kong. Trade doesn't hurt either. But I don't think most people know about that. Instead I recall reading an article about Taiwanese actors being in other countries (like China) and having an interview about how they learned a totally different culture from one area of China to another.
Macau. Many people know for the same reason as Hong Kong. (Though under I think Portugal). Not to mention Hong Kong loves to go to Macau for a cheap and fun trip.
Philippines. EVERYONE knows in this area. Their culture is so influenced by Americans. They know it. They love looking up things about America.
Now, I can't speak for Korea or Thailand since I have never been there myself and if you have any other Asian country you want to list. Go for it. But pulling one or two names out of all the countries means nothing.
And back on the kid issue.
I know you're just going to argue to "not always" card anyways. So fuck you, sit down and listen for a moment before everything goes out the other ear.
As my examples were stating. Media is the big driver of what children know. School as well... but not as much.
Media. Most of us who grew up with North American media will concur that media nowadays is much more fucked up than it was a decade ago. No matter how silly, it wasn't really retarded. No matter how crazy, it didn't look like an acid trip. I have no doubt in my mind that Hannah Montana, Dave the Barbarian and Spongebob are teaching our children to be great. Dora might be a good example... but I don't know. Bob the Builder might be likeable though.
But seriously. Spongebob is an acid trip into the realm of mental stupidity. The only cartoon I can think of that I saw when young that was just as "holy shit that's crazy", was the Magic School bus. And that shit was educational.
We had to rename Sesame Street to Sesame Park. Because playing on streets is a bad idea. WTF?
My generation went from the "lets play with lego/k'nex"/read or be imaginative to the generation where even 4 year old children play video games. Not to mention they know more about how to spend money than to make it. Fuck, I had to save up allowance for a month just to come close to buying things I wanted.
True, situations may arise where North American kids may "survive better" than their "equal counterpart" in Asia. But let's talk averages. Sure, camping is a fucking useful thing to have experienced. But how much of a percent of American children can admit to haven experienced this let alone going outside for regular physical activity?
Also, make a fair comparison. Every middle class kid in America has an advantage to slum kids in Asia. I'm talking Ghetto vs Ghetto, Middle class to middle class and High class to high class.