The site asks you to pick a random number, not mentioning anything about trying to achieve a specific distribution.
EDIT: Downvotes and no comments, nice. You guys seem to be misunderstanding something. If asked to picked any number ("random") between 1 and 10, to suggest that the outcome is "wrong" because the distribution isn't uniform doesn't make any sense at all. It would be a completely different experiment if we were asked to pick a number between 1 and 10 such that the outcome after x number of independent trials has a uniform (or gaussian/exponential/etc) distribution. This seems to be what some people are assuming.
The point of probability is to describe uncertain events. Coin flips aren't described by uniform distributions, they're binomial. Human intelligence can be modeled by a Gaussian distribution. And this site's experiment seems to suggest that picking a number between 1 and 10 can be modeled by a bimodal random variable with means around 4 and 7. Point being: random doesn't necessarily mean uniform.
No, but random does mean uncertain, and the uniform distribution has maximal entropy. In other words, uniformly distributed numbers are most random, colloquially, and so you can improve your ability to generate random numbers by sampling from a more unform distribution.
Also, just because intelligence is described with normal distributions, it is not at clear that it can be.
This comes from the fact that the first run of six 9's in the digits of pi comes much sooner than expected: http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.htm... search for 999999 - you'll see it's only 10 lines down. When discovered, this caused a lot of people to conclude that the digits were not random. Of course, with 5 trillion digits now calculated, there is still no bias found toward any pattern. So it is very hard to tell!
The larger the sample, the more likely a truly random input approaches a uniform distribution. Yes, a coin flip could come up heads 10000 times in a row, but it just doesn't happen.
Benford's law applies to those cases where you can assume that the logarithms of the numbers are uniformly distributed.
While it's perfectly reasonable to assume that for, let's say, Microsoft's yearly revenue, Apple's stock price, or a number series with x% average growth (for example, inflation-affected prices), it has nothing to do with this experiment.
