Your assumptions may be ok, but your final point is wrong. As i read, you said poverty is caused because because bad rich distribution, its ok, but you said (implicity) Bill Gates is who generate all this.
Ill tell you something, the main source of BG money is not the license you buy of windows. Its interest, inversions and good bussines.
Your example was not bad in general, but you are forgotting something. In long term, the guy who has 65 cant hold his money without keeping investing. The 2 guys who invent thing will keep earing money as new products are researched, and the 7 guys will stop buying as they cant get another source of money.
In real economy, those who buy software use it to generate more money, its not wasted money, any serious bussines knows that, that why the MS SOs ratio is still high.
BG money is not "saved" money neighter. BG has very low "stoped" money inside some safe (he is not McDuck, he doesnt swimms on coins) all the BG money is paying reserchers, and saving the US economy (builds, banks, taxes, roads).
Economy is not so simple and there was always poor people.