Fun fact: “actual doctor-administrated” IQ tests can vary by 15+ points depending on which location you go to. This goes for MENSA official testing locations, and MENSA claims to be extremely prestigious and exclusive. Online IQ tests are an absolute joke (even MENSA’s practice test), and in-person ones are highly variable and not particular accurate. Even IQ itself is indicative of literally nothing meaningful, and certainly not intelligence.
I have taken a professional IQ test before, as well as various online IQ tests, and the numbers I get are generally quite consistent (which is the mark of a good psychological test). I always get results in a 20 point range. Out of my friends that have done IQ tests, they also generally get the numbers I would expect (again landing in a 20 point range). This is all anecdotal, but it seems unlikely to me that the tests would seem to work so well in the cases I know of if they were actually just random or extremely inaccurate. Of course, there is variance, but I think that you can have some confidence that your true IQ lies within 10-20 points of your score, especially if you have done a few different tests, which is a big range, but not trivial.
In terms of IQ itself, I don't think it's fair to say that it's indicative of "literally nothing meaningful." From what I understand, it is the best single predictor for a person's success (financially). Mandatory disclaimer that, obviously, IQ has nothing to do with your value as a person, if only for the fact that you did nothing to deserve your IQ. Some people fixate too much on IQ and I understand there's a lot of debate about the technicalities of IQ, but insofar as people generally understand that some people are smarter than others, I've never heard of a good argument for why IQ is not a decent way to quantify that intuition.
It seems clear to me that speedsolving would correlate with IQ or intelligence more broadly. Pattern recognition is the most obvious. IQ tests also often test spatial reasoning and memory.
If you look up various top cubers of the past or present, you'll find that they are disproportionately successful, mostly in STEM fields. Off the top of my head, I know that Collin Burns works for OpenAI and Kevin Hays has worked for several FAANG companies. I used to participate in math competitions, and I know a lot of people from that who were into cubing as well (notably someone who went to the International Math Olympiad was also an AsR holder in big cubes). To me, there seems to be a lot of empirical and theoretical reasons to believe that there is a correlation between the two (here I'm taking for granted that high performance in STEM correlates with IQ score).