  The observed internal plateau of X-ray emission in some short GRBs suggests
the formation of a remnant supra-massive magnetar following a double neutron
star (NS) merger. In this paper, we assume that the rotational energy is lost
mainly via gravitational wave (GW) radiation instead of magnetic dipole (MD)
radiation, and present further constraints on the NS nuclear equation of state
(EoS) via mass quadrupole deformation and r-mode fluid oscillations of the
magnetar. We present two short GRBs with measured redshifts, 101219A and
160821B, whose X-ray light curves exhibit an internal plateau. This suggests
that a supra-massive NS may survive as the central engine. By considering
twelve NS EoSs, within the mass quadrupole deformation scenario we find that
the GM1, DD2, and DDME2 models give an $M_{\rm p}$ band falling within the
2$\sigma$ region of the proto-magnetar mass distribution for
$\varepsilon=0.01$. This is consistent with the constraints from the MD
radiation dominated model of rotational energy loss. However, for an r-mode
fluid oscillation model with $\alpha=0.1$ the data suggest that the NS EOS is
close to the Shen and APR models, which is obviously different from the MD
radiation dominated and mass quadrupole deformation cases.
