Background: The observation of the superdeformed (SD) bands in $^{60,62}$Zn indicates a strong SD-shell effect at the particle numbers 30 and 32, where two and four neutron single-particles are considered to be promoted to the intruder $1g_{9/2}$ shell. However, the SD-yrast band in $^{62}$Zn is assigned negative parity. Purpose: I investigate various SD configurations in the rapidly rotating $^{60,62}$Zn isotopes, and attempt elucidating the different roles of the SD magic numbers 30 and 32. Method: I employ a nuclear energy-density functional (EDF) method: the configuration-constrained cranked Skyrme-Kohn-Sham approach is used to describe the rotational bands near the yrast line. Results: I find that the neutron number 32 favors stronger deformation than 30; a competing shell effect of protons and neutrons makes the SD-yrast structures of $^{62}$Zn unique. Due to the coherent shell effect, the positive-parity band emerges in $^{64}$Ge as an SD-yrast band with greater deformation than that in $^{60,62}$Zn. Furthermore, the present calculation predicts the occurrence of the hyperdeformed (HD) magic numbers 30 and 32 at a high rotational frequency $sim 2.0$ MeV$/hbar$. Conclusions: The negative-parity SD bands appear higher in energy than the positive-parity SD-yrast band in $^{60}$Zn and $^{64}$Ge, indicating that both the particle numbers 30 and 32 are SD magic numbers. The positive-parity HD states appear as the yrast band at $I sim 50hbar$ in $^{60}$Zn and $^{64}$Ge. The particle numbers 30 and 32 are magic numbers of SD and HD.
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