Stellar kinematics provide insights into the masses and formation histories of galaxies. At high redshifts, spatially resolving the stellar kinematics of quiescent galaxies is challenging due to their compact sizes. Using deep near-infrared spectroscopy, we have measured the resolved stellar kinematics of four quiescent galaxies at z=1.95-2.64, introduced in Paper I, that are gravitationally lensed by galaxy clusters. Analyses of two of these have previously been reported individually by Newman et al. and Toft et al., and for the latter we present new observations. All four galaxies show significant rotation and can be classified as fast rotators. In the three systems for which the lensing constraints permit a reconstruction of the source, we find that all are likely to be highly flattened (intrinsic ellipticities of $approx0.75-0.85$) disk-dominated galaxies with rapid rotation speeds of $V_{rm max}=290-352$ km/s and predominantly rotational support, as indicated by the ratio $(V/sigma)_{R_e}=1.7-2.3$. Compared to coeval star-forming galaxies of similar mass, the quiescent galaxies have smaller $V/sigma$. Given their high masses $M_{rm dyn} gtrsim 2times10^{11} M_{odot}$, we argue that these galaxies are likely to evolve into slow rotator elliptical galaxies whose specific angular momentum is reduced by a factor of 5-10. This provides strong evidence for merger-driven evolution of massive galaxies after quenching. Consistent with indirect evidence from earlier morphological studies, our small but unique sample suggests that the kinematic transformations that produced round, dispersion-supported elliptical galaxies were not generally coincident with quenching. Such galaxies probably emerged later via mergers that increased their masses and sizes while also eroding their rotational support.
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