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!

He's comparing apples to apples. Kolmogorov complexity for different ways to approximate п is more or less flat at bang for the buck.

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.