I'm not sure I agree with this at all. This seems to be an attempt to conflate correlation and causation, for one thing; just because the number of people living under the poverty level has fallen (assuming that's right; I haven't checked it) while income inequality has risen doesn't mean income inequality is what caused the standard of living for the poor to rise. In fact it's far more likely that it's the social safety net programs started in the 60s that have accomplished the latter.
Also, I'm not sure it's necessarily right that "the poor have slowly increased their wealth" over time. The Pew data here (
1. Trends in income and wealth inequality) show that when adjusting for inflation, the median wealth of lower-income families actually went
down between 1983 and 2016 (it went up substantially 1983 through 2001, then down even more substantially from 2001 to 2016). While the wealth of upper-income families has steadily risen; in that same time period upper-income families went from holding under 60% of the nation's wealth to holding over 80%. I don't see the current data so maybe that has now recovered to the point where the median wealth of the poor today is higher, in inflation-adjusted dollars, than in 1983.