I can tell you two things:
1. You have lost a great thing to learn about our issues.
2. Don't inquire further into them. If things keep up, I'm pretty sure listening to America's politics is going to become the number one cause of suicide in the next few years.
OK, joking aside, the basis is that the United States government is heavily in debt.[footnote]Just as a side note, it is been a while since I seriously looked into this issue, at least on the level of having to write about it. If anything has changed from what I've said, or if I'm messing up my economics, feel free to correct me.[/footnote] If you want to get an idea of how bad, just watch this clock [http://www.usdebtclock.org/] and compare our debt to GDP. Some of our debt is owed to China, some to Japan, some to U.S. citizens, some to programs within the U.S., and a bunch of other areas (i.e. the idea that all of our debt is in China is false, though a lot of it is there). The problems that further arise are:
1. The American government, whether you're dealing with Republicans or Democrats, is horrible at dealing with the deficit (the amount we lose every year), and as a result, the debt (the total amount we owe) is constantly increasing. We haven't had a surplus since 2001! And before that, we had pretty much been on a streak of decades of debt accumulation until Clinton brought us to a surplus in 1999.
2. The American population, no matter how much they clamor for wanting to lower the debt, isn't willing to lower the debt. I can't find it now, but around 2011 Pew Research did a survey and found that Americans didn't want to increase taxes on themselves, but they also didn't want to decrease spending on anything except foreign aid. In other words, no matter what Americans say they want, if the questions are asked correctly, they really want lower taxes and higher spending. Do the math. It doesn't work.
3. The American government is in complete gridlock, provided it is even working to begin with. Both sides are so hard set on their ideologies that they practically refuse to work together.
4. Considering the way American government is set up and the current political divide between Republicans and Democrats, don't expect this problem to sort itself out any time soon.
As for whether or not China controls us, it's up for debate. Some will cite how "the debtor is servant to the lender" while others will point out that China relies on our consumerism to run its own economy (pretty much everything over here is made in China unless the company making it ascribes to the "Made in U.S.A." campaign). I don't know enough about the relationship between the two to really know how it will play out. My guess is China won't bother to tear us down with our own debt until their economy no longer has any use for the U.S.
As for how it will affect the video game industry, it's hard to tell. Government shutdown won't prevent games from being made or rated, as games are designed by private companies and the ESRB is an organization unaffiliated with the government. After that, it really depends on how companies can handle Obamacare, as well as how people will respond in tough economic times. Certain markets are comparatively unaffected by issues like unemployment, recession, and similar issues. [footnote]An interesting note is that some markets actually do better in tough economic times, but I doubt the gaming industry will fall under that category, given that games are a luxury item.[/footnote] Ultimately, it depends on how game companies can handle tougher economic times, and that's based on whether or not people want to spend during those times. Keep in mind, we've been doing better on unemployment over the last few years [http://data.bls.gov/timeseries/LNS14000000],[footnote]Do bear in mind that unemployment is somewhat hard to track in the U.S. There are certain conditions one has to meet to be considered "unemployed", and those conditions don't cover everyone who is actually unemployed. For all we know. In other words, unemployment is much higher than in that link, but again, we can't track it, so we can't really factor that in, nor do we really know if it has been seriously increasing as the official unemployment rate drops.[/footnote] even if we're still not doing good on it. Unfortunately, I really don't know much about how the shutdown will affect all these economic issues and, as a result, indirectly affect the video game industry.
Now, if the U.S. is forced to default on its debt...yeah, we'll have some issues.