Textbook confusion with CMRR and transconductance mismatch
The two equations subtly encode different assumptions and do not contradict each other. When you use \$g_{m}=\mu _{n}C_{ox}\frac{W}{L}V_{OV}\$ to estimate the error in \$g_m\$, you are looking for the effect of errors in the shape ratio on the transconductance, with overdrive voltage held constant (and thus drain current varying as the shape ratio varies).
On the other hand, when you use \$g_m = \sqrt{2(\mu_n C_{ox})\left(\frac{W}{L}\right)I_d}\$, you are looking for the effect of shape ratio on transconductance, with drain current held constant (and overdrive voltage varying to make this happen, e.g. in a structure with feedback). Since the square root of 1.02 is approximately 1.01 as already pointed out in the comments, we get the 1% error which is expected.
This equation here is useful in many scenarios where the drain current is held constant (e.g. in the scenario given in the text, as well as in a common source amplifier biased with a current source, and with the gate voltage's DC bias established through feedback).