  We estimate kinematical higher-twist (up to twist 4) corrections to the
$\gamma^*(q_1) \gamma(q_2) \to M(p_1) \bar{M}(p_2)$ amplitudes at large
$Q^2=-q_1^2$ and small $s=(q_1+q_2)^2$, where $M$ is a scalar or pseudoscalar
meson. This process is known to factorize at leading twist into a
perturbatively calculable coefficient function and generalized distribution
amplitudes (GDAs). The kinematical higher-twist contributions of order $s/Q^2$
and $m^2/Q^2$ turn out to be important in the cross section, considering the
kinematics accessible at Belle and Belle II. We present numerical estimates for
the cross section for $\gamma^* \gamma \to \pi^0 \pi^0$ with the $\pi \pi$ GDA
extracted from Belle measurements and with the asymptotic $\pi \pi$ GDA as
inputs to study the magnitude of the kinematical corrections. To see how the
target mass corrections of order $m^2/Q^2$ affect the cross section, we also
perform the calculation for $\gamma^* \gamma \to \eta \eta$ by using a model
$\eta \eta$ GDA.In the range $s> 1$ GeV$^2$, the kinematical higher-twist
corrections account for $\sim 15 \%$ of the total cross section, an effect
which is not negligible. Since $\pi \pi$ GDAs are the best way to access the
pion energy-momentum tensor (EMT), our study demonstrates that an accurate
evaluation of EMT form factors requires the inclusion of kinematical
higher-twist contributions.
