Rogowski coil response factor frequency dependence
I guess the response factor \$k\$ is defined for amplitudes of sinusoidal steady state signals of the given frequencies (50Hz and 60Hz).

\$V_0 = k I_0\$ where
\$I_0\$ is amplitude of sinusoidal current signal \$I(t) = I_0 sin(\omega t)\$ and
\$V_0\$ is amplitude of sinusoidal voltage singal (output)

Then the quotient of the given response factors 2.4 / 2.0 = 1.2 is exactly what you expect from the formula 60Hz/50Hz = 1.2.

Your formula from Wikipedia is frequency depedent: the frequency dendency is given by the d/dt operator: the higher the frequency (of the I(t) signal), the higher is the rate of change even if current amplitudes are the same:

\$I(t) = I_0 \sin(\omega t)\$ &rarr; \$\frac{d}{dt}I(t) = I_0\omega \cos(\omega t)\$
i.e. amplitude of rate of change is \$I_0\omega\$, directly depedent of frequency.