Correct. Except, the poor won’t be the new rich because there are more poor than rich. Many, many more. Hence the idea that the way things currently are is unfair.
Take the money from the rich, give it to the poor and we will have something slightly closer to economic equality.
Perhaps you already know this but while the simple minds version isn’t a cover, they didn’t write it.
It was written for them by a composer and a producer pair.