1) Does gig mean "a temporary job"?
Usually, but in this case I think catebrad00 might be referring to just a job in general (with no regard for temporariness).
2) Does way back mean "long ago"?
I believe that sentence was wrongly broken into two separate sentences, which do not make sense as separate halves.
Try this: "Way back, when the government made it illegal for the rich to send their kids to international schools, you had to be international. So rich Chinese people and others started building private schools and hiring expatriate teachers."