A simple explanation is that "randomness" here is related to (logarithm of) the minimum average time [1] you would take to guess the password correctly (H=sum(pi * log(1/pi)). Since the random number generator supposedly gives an uniform distribution over a set of words, this simplifies to H=n(1/n log(n))=log(n).

[1] Your average time is at least t* =1/2 * 2^H, so log( t* )>H-1.