This probability function $P(k,n)$ represents the fraction of games which we expect to yield k heads, in the toss of n coins.
$P(k,n)=\frac{\binom{n}{k}}{2^{n}}$
The author of the book i'm reading says that the dashed curve of this figure passes through the points computed from 100 · P(k,30)
The shape of this distribution ( 100 · P(k,30) ) is a gaussian one. Is this a consequence of the CLT or has it got nothing to do with it?
Comment continued: The illustration in your Question does not show enough plays of the game (consisting of $n = 30$ tosses of a fair coin) to give an ideal impression of the binomial and normal distributions. [In the same way, selecting only 100 men from a population where heights average 68" with SD 3.5" cannot be expected to give a 'smooth' histogram closely resembling a normal curve.]
With $n = 30$ tosses binomial distribution is well-approximated by a normal distribution. But with only a few plays of the game, the sample isn't large enough to show a good approximation of results to either the binomial model or the normal approximation.
Here is a histogram resulting from 10,000 plays of the 30-toss game. The curve is the density of $\mathsf{Norm}(15, \sqrt{30/4})$ and the red dots show the exact distribution of $\mathsf{Binom}(30, 1/2).$
To illustrate that relatively large sample sizes are necessary for smooth histograms, here are histograms of simulated samples of 100 and 10,000 men respectively. (Textbook examples with small samples are often carefully chosen or contrived to make nice histograms, but for actual real-world data, larger sample sizes are usually required.)