I think the point is that McLoone is using two different notations and measuring an artifact of this. There's nothing special about base-10 denominators.
Perhaps we could say he's comparing Shannon entropy per symbol for the two systems.
It seems that what's special about rationals with power-of-10 (with power > 1) denominators is that we have a readily available shorthand, uh notation, for them.
Notation can be very significant. The transition from Roman numberals to positional notation with 0 took a thousand or so years. But boy did it ever make long division easier!
Strictly speaking it is not Kolmogorov complexity (That has an upper bound, namely the constant size of a program that can output arbitrarily many digits of Pi.)
Kolmogorov complexity requires a standard Turing machine to measure -- switching notations isn't allowed. Rational approximations to Pi (or any other irrational number) vary substantially in terms of accuracy/size, which is why many standard libraries include functions for computing convergents.
