It has a time limit, so it does measure how quick you are.
So it probably bakes in a range. Like if you complete this test in the allotted time, you will be in this range. But if you completed it in half the time, you'd probably be higher, but they haven't calculated the range you'd be in. They'd just say, "Yeah, you're in the top range".
There are awards, patents, accomplishments, etc.
There are positive correlations between IQ and positive outcomes in general. Basically, take a metric of success and group people into it and you'll find people with higher IQs in the groups with better outcomes.
Even if you then slice those groups by other factors.
Second, why would we even have to cut off the tail portion?
Next, you didn't cover that contingency. You keep saying it's all income levels, but it's not. IQ and positive outcomes are positively correlated. Pick a thing, pick a measure of success, you'll find that people with higher IQs will tend towards the successful group.
And this is also a "all doctors are tall, not all tall people are doctors" kind of statistic. Higher IQ people will wind up in the more successful groups more often, but being in the more successful group doesn't mean you have a high IQ.
Pattern recognition is a large part of that. A person who is able to discern patterns more easily, is usually able to reason better. More able to do second and third order thinking.
IQ "tests" that use words or numbers are also testing knowledge to some degree, which isn't something you typically want when you want to test raw intelligence. Being able to do calculus doesn't necessarily prove you're intelligent, it proves you know calculus.
So that leaves abstract concepts. And that's another facet of intelligence, being able to think abstractly. There should also be some "die folding" questions in there. Where it shows you six connected boxes and you pick the cube that it makes. That one is also about spatial relations as you have to model the cube in your head in some fashion.
All that being said: intelligence is nothing on its own. It's a force multiplier. Intelligence allows you to use the knowledge and skills you do have better. It also makes the acquisition of knowledge and skills easier. People with higher IQs have better life outcomes on average than those with lower IQs among every cohort. What that means, if you take all the poor people, those poor people with higher IQs are going to be doing better overall. Still poor, but able to make more of what they have. Tall people? People with higher IQs will be doing better overall than those with lower IQs. Doctors? Same. Welders? Same.
Now, this doesn't mean that every person with a higher IQ is doing better. Success is very multi-faceted and dependent on a lot of things, some of which are outside of our control entirely. But it helps.