  Recent reports claiming association of the massive star binary system
$\gamma^2 $Velorum (WR 11) with a high-energy $\gamma$-ray source observed by
\textit{Fermi}-LAT contrast the so-far exclusive role of $\eta$ Carinae as the
hitherto only detected $\gamma$-ray emitter in the source class of
particle-accelerating colliding-wind binary (CWB) systems. We offer support to
this claim of association by providing dedicated model predictions for the
nonthermal photon emission spectrum of $\gamma^2$ Velorum.
  We use three-dimensional magneto-hydrodynamic modeling (MHD) to investigate
the structure and conditions of the wind-collision region (WCR) of $\gamma^2$
Velorum including the important effect of radiative braking in the stellar
winds. A transport equation is then solved throughout the computational domain
to study the propagation of relativistic electrons and protons. The resulting
distributions of particles are subsequently used to compute nonthermal photon
emission components.
  In agreement with observation in X-ray spectroscopy, our simulations yield a
large shock-cone opening angle. We find the nonthermal $\gamma$-ray emission of
$\gamma^2$ Velorum to be of hadronic origin owing to the strong radiation
fields in the binary system which inhibit the acceleration of electrons to
energies sufficiently high for efficient inverse Compton radiation. We also
discuss the strong dependence of a hadronic $\gamma$-ray component on the
energy-dependent diffusion used in the simulations. Of two mass-loss rates for
the WR star found in literature, only the higher one is able to accommodate the
observed $\gamma$-ray spectrum with reasonable values for important simulation
parameters such as the injection ratio of high-energy particles within the WCR.
