It is said that Codeforces rating is much more inflated than chess.com and FIDE rating, however similar to lichess.com ratings. This can be observed from the top ratings of each site and some online chess/lichess/FIDE rating converters.

I think that there is only one meta-analysis summarizing the relationship between cognitive ability (and broad cognitive abilities) and chess skill (it is a pretty short article). Basically, the study found that the correlations between broad cognitive abilities (fluid reasoning, short-term memory, crystallized intelligence, and processing speed) were all around $$$r = .24$$$. Keep in mind that this does not account for restriction of range (the average elo standard deviation of the studies used in the analysis was around $$$\frac{3}{4}$$$ of the sd of the general chess population). But, according to the authors, this shouldn't affect the correlations too much.

Anyway, excluding one anomalous study, they found that the correlation between general cognitive ability and chess skill was also around $$$r = .24$$$. The average IQ in the studies used here was $$$120$$$ and the sd was right around $$$15$$$, so there was really no restriction of range, at least wrt $$$IQ$$$. Now I believe that this correlation is a bit of an underestimate considering the fact that the broad cognitive abilities all had similar correlations with chess skill. For specific skills (chess, codeforces, video games), it is usually the case that general cognitive ability has a higher correlation with the skill than any of the broad and specific cognitive abilities. So, since the broad abilities all had correlations of $$$r = .24$$$ (even with range restriction), and since they had more studies to back them up (they have more reliable effect sizes), I think that it is fair to say that the correlation between chess skill and cognitive ability is closer to $$$r = .3$$$ in the population of $$$120\,\,IQ$$$, sd $$$15$$$ chess players. Let's just say it is $$$r = .3$$$.

No one knows the correlation between cf skill (rating) and $$$IQ$$$, but I think that the one study done on it shows that the correlation is clearly higher than $$$r = .3$$$. In fact, the correlation could be higher than $$$r = .5$$$.

An interesting thing you can see about this study is that the highest $$$r^2$$$ belongs to the composite $$$IQ$$$ vs rating plot. This falls in line with the fact that general cognitive ability usually has the highest correlation with some specific skill over all cognitive abilities. So it's really not that interesting. Now the correlation here is $$$\sqrt{.1865} \to r \approx .43$$$.

But this is almost certainly an underestimate, because the test that was used was bad. The test has a correlation of $$$r = .57$$$ with the WAIS-II (on a more or less representative population), which was a professional $$$IQ$$$ test. Anyway, this correlation is pretty bad. Correlations between modern professional $$$IQ$$$ tests should be $$$r \ge .8$$$.

Now, given the content of the test (you can take it yourself if you would like), I think that it is a fair assessment that the only significant factor that cf skill and the test have in common is that they both measure intelligence to some degree. Because the test is a somewhat poor measure of intelligence, you'd expect the correlation between cf skill and the FSIQ score obtained from the test to be lower than the correlation between cf skill and general cognitive ability, as there are more specific factors measured by the test but not necessarily by cf skill (because of its low accuracy). Furthermore, the fact that native and nonnative English speakers were grouped together would also lower the correlation, but probably not substantially. So I think that this shows that the correlation could definitely be higher than $$$r = .5$$$.

I don't think the author of the blogpost reports a mean $$$IQ$$$, but it looks to be around $$$120$$$. Again, this is probably a slight underestimate, because of the low accuracy of the test. Imagine you took a bunch of cf users and gave them a very specific test about cars (which has nothing in common with codeforces skill except for its slight correlation with general intelligence). You'd expect them to score just about average on that test. Following this logic, you'd expect the users to score higher than $$$120$$$ on a test that measured general cognitive ability better than the OpenPsychometrics test. What's more is that the nonnative English speakers would bring down the average just a touch.

Now the correlation between cf skill and gca is far from determined, but I think that $$$r \approx .5$$$ is a decent approximation. Now, from the sample in the meta-analysis, the average chess player's $$$IQ$$$ is around $$$120$$$. From the cf study, it looks like the average $$$IQ$$$ of those who participated (who are more skilled than the average cf user) is around $$$125$$$ if I were to guess.

Another important finding in the study of chess skill and gca is that the correlation between the two tends to decrease as chess skill increases. So the average $$$IQ$$$ of someone rated $$$2000$$$ is not much different than the average $$$IQ$$$ of someone rated $$$2400$$$. This reflects a larger pattern known as Spearman's law of diminishing returns, which states that gca is a worse predictor for high performers than for low performers. This almost certainly holds true for cf skill, meaning that there might not be much of an $$$IQ$$$ difference between $$$2400$$$ and $$$3000$$$ rated users, on average.

Now, although it is true that a gm in chess is quite a bit further away from the mean chess study participant when compared with a cf gm from the mean cf study participant, this shouldn't matter too much wrt how much higher the chess gms' $$$IQs$$$ actually are because of this difference, because the two gms are both relatively high enough that going any higher really doesn't change the $$$IQ$$$ s all that much because of the general truth of Spearman's law of diminishing returns. But we can say that there is certainly a stronger correlation between cf skill and $$$IQ$$$ than chess skill and $$$IQ$$$. Plus, it also seems like those who participated in the cf study had slightly higher $$$IQ$$$s than those who participated in the chess studies analyzed in the meta-analysis. Therefore, it is highly likely that the average cf gm has a higher $$$IQ$$$ than the average chess gm.