  The enigmatic X-ray emission from the bright optical star, $\gamma$
Cassiopeia, is a long-standing problem. $\gamma$ Cas is known to be a binary
system consisting of a Be-type star and a low-mass ($M\sim 1\,M_\odot$)
companion of unknown nature orbiting in the Be-disk plane. Here we apply the
quasi-spherical accretion theory onto a compact magnetized star and show that
if the low-mass companion of $\gamma$ Cas is a fast spinning neutron star, the
key observational signatures of $\gamma$ Cas are remarkably well reproduced.
Direct accretion onto this fast rotating neutron star is impeded by the
propeller mechanism. In this case, around the neutron star magnetosphere a hot
shell is formed that emits thermal X-rays in qualitative and quantitative
agreement with observed properties of the X-ray emission from $\gamma$ Cas. We
suggest that $\gamma$ Cas and its analogs constitute a new subclass of Be-type
X-ray binaries hosting rapidly rotating neutron stars formed in supernova
explosions with small kicks. The subsequent evolutionary stage of $\gamma$ Cas
and its analogs should be the X Per-type binaries comprising low-luminosity
slowly rotating X-ray pulsars. The model explains the enigmatic X-ray emission
from $\gamma$ Cas, and also establishes evolutionary connections between
various types of rotating magnetized neutron stars in Be-binaries.
