"The economy is not a zero-sum game. This is not a race to the bottom. As low cost-of-living places get more and more jobs, their standard of living rises and costs go up accordingly."
No, it is not a zero sum game, it is more like a steam engine: it requieres a hot (cheap producers) and a cold spot (rich consumers) to work.
Now, the game big corps are trying to play is to find if they are able to jump from hot spot to hot spot and the world will be big enough so by the time the travel it around (from Japan to Korea, from there to China, India and Philippines, from there to Brazil and Latin America, from there to Africa) old hot spots are already cold again (...and once Africa becomes hot enogh, back to, say, India, which by that time is again as poor as it was in the begining).
"And don't overlook the key fact that more people buy a given product than work to make it."
Just like in the steam engine example, you won't be able to extract more energy (wealth) than you put in. It is not a zero-sum game but it still is a closed-system one. More people buy a given product than it takes to produce it... provided they have the money to buy it, which comes in turn from the money those other people have earned by doing things that other people can and want to buy (which ones? the first ones? no, they don't have the money because all they have is just the portion the second group already gave him, which must be less than their own surplus, or else they'd be producing that themselves at an advantage).
"Walmart selling lots of stuff made in China. The total amount saved by all Americans in buying these products is several times larger than the total lost wages."
For one, it's not clear for that to be the case. For another, it is only savings if they were in the need of buying that even at a higher price, which for the most part is not the case. I'd call that the "promotional sale" fallacy.