Why doesn't the trade balance equation take into account the value of products sold by the U.S.? $$NX ≡ (S-I) + (T-G)$$
  Read this as “the trade balance (net exports) is identical to the sum of net savings (savings minus investment) and the government’s budget surplus or deficit (taxes minus spending).” This is not a theory of what causes what; it’s an identity, different ways of expressing the same “what”.


Let's say the U.S. had a $NX$ or trade deficit of $500$ billion dollars and overnight the U.S. forced countries around the world to buy $1$ trillion dollars of U.S. military equipment giving the U.S. a trade surplus of $500$ billion. Does this mean that the equation: $NX ≡ (S-I) + (T-G)$ doesn't take into account non-macroeconomics factors and therefore is wrong?
If foreign countries suddenly bought $\$1$ trillion worth of stuff, presumably the US would supply this out of existing inventories (i.e. stocks of goods).  

Before anything else happens, this represents a reduction of investment in the US and your equation would continue to balance since the increase in $NX$ would be offset by a reduction in $I$ (which has a negative sign in your national accounts identity).  

What would happen next is probably that the manufacturers would make more stuff to bring inventories back towards previous levels, increasing investment. They and their workers may pay taxes on their income.  They may import some more stuff.  What is left may add to savings.  But throughout this process the national accounts identity will remain true.