You are fixed on that IQ stat, talking about it as some kind of metric and even doing math with it, but you fail to understand what the metric means. Even such a simple thing as running speed is not that simple. One might say it measures muscle strength, or "the capability of your body", while really it measures a combination of muscle strength, tendon elasticity and nervous system fitness (or running skill). Now we see that if you don't know HOW to run, you might be even stronger and still run slower than more skilled weaker runner.

Now IQ. Let's look at the test. What you see is many different kind of questions. Pattern matching for language, geometry and numbers generally. What does it mean that you answer those questions correctly? It means you are good at matching patterns in words, shapes and you know math a little. That's it. It doesn't show anything more than that. Those skills does not even directly transfer to other areas.

Your exclusion of hyper-specialized people like professional chess player is actually hitting the spot on the point here - high IQ people are just hyper-specialized on IQ tests (I bet many of them practiced to solve them multiple times) and generally tasks that require pattern matching. It doesn't mean you can do math, that you know chemistry, politics, that you know how to communicate with people or what to do with money. Those are all learned.

If you can make analogy of brain as car, and the "life achievement" as distance traveled, then IQ would just be the speed, or power of the car. What flows from this is that you don't magically appear from NY to LA when you get a faster car (you are of higher IQ) than other people. It just means that if you go to LA with it, you might come there a little faster. This also means that anyone with lower IQ can achieve same things, it just takes a little more time.

Now, same as driving further even with slower car, or running faster (if you are more skilled runner) than stronger runner, people can also be more intelligent even while having lower IQ just by knowing more, having more experience and having more skill. Because they have spent much more time excelling these skills. That's why I don't even think it should be called IQ, I think it should be changed to PMC (Pattern Matching Coefficient), because it doesn't measure intelligence at all. Besides, when talking about intelligence, one must specify what narrow area you are talking about, otherwise it doesn't even make sense on it's own.