Measuring entropy of a uniform distribution source
In cryptography and information theory, Shannon entropy $H(X)$ is a characteristic of a source $X$ of discrete symbols; e.g. a characteristic of a dice. It's usually expressed per symbol produced, and with unit the bit (per symbol). It tells the expected/average number of bits necessary to encode the value of a symbol, knowing the characteristics of the source. In particular, the entropy of a known¹ deterministic source (such as a Pseudo Random Number Generator with known¹ seed) is $0$.
Assuming the symbols can take values $x_i$, are produced independently at random (that is, earlier outcomes have no influence on later ones), and each symbol $x_i$ has fixed probability $p(x_i)\ge0$ with $1=\sum p(x_i)$, then
$$H(X)=\ \sum_{i\text{ with }p(x_i)\ne0}p_i\,\log_2\frac1{p(x_i)}$$
For example, a fair dice has entropy $H(X)=6\,\left(\frac16\log_26\right)=\log_26\approx2.585\ldots\,$bit/symbol. Another dice, biased towards generating 6 with probability $1/5$, and the 5 other sides having probability $4/25$, has $H(X)=\frac15\log_25\,+5\,\left(\frac4{25}\log_2\frac{25}4\right)\approx2.579\ldots\,$bit/symbol.
This illustrate the fact that for a given number $n$ of symbols, entropy per symbol is maximal at $\log_2 n\,$bit/symbol when all the symbols have the same probability, that is uniform distribution. The article mentioned in the question has it right!
Intuitive justification: when things have a high probability to be in a corner (uneven distribution), there is less disorder/entropy than when they are spread evenly all around. In the later case it takes more information to describe where each thing is.

¹ What happens if we remove known is a matter of perspective. Any PRNG implementable with finite resources has zero entropy, for we can define all it's output with a finite amount of data. On the other hand, for practical adversaries, a Cryptographically Secure PRNG that outputs integers symbols in $[0,n)$ is indistinguishable from a true RNG with entropy of $\log_2 n\,$bit per symbol and the same output domain.