You have the cause and effect switched. More intelligent parents have higher incomes, their kids also are more likely to have higher intelligence because it's heritable. So if a bunch of rich Jews live in a Manhattan, does it mean that IQ is predicting their zip code? Or is it predicting they are Jewish? That's just a weird way of thinking about it.

Your definition of intelligence is not that is commonly thought of intelligence. It's like saying "intelligence is your maximum chess skill measured by elo and you will never achieve it"

But learning to play chess quickly would also fall under intelligence. Given not being a high level at a similar game, there will be people who learn quicker than others. Learning languages, learning from your experience, all fall under intelligence.

If you take all of these measures, average them, you will get a true intelligence measurement. IQ is a sample of true intelligence by using only some measurements, since intelligence can have an infinite amount of tasks that it can be used to perform