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 ($Msim 1,M_odot$) 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.
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