  The Dusty S-cluster Object (DSO/G2) orbiting the supermassive black hole (Sgr
A*) in the Galactic centre has been monitored in both near-infrared continuum
and line emission. There has been a dispute about the character and the
compactness of the object: interpreting it as either a gas cloud or a
dust-enshrouded star. A recent analysis of polarimetry data in $K_{\rm s}$-band
($2.2\,{\rm \mu m}$) allows us to put further constraints on the geometry of
the DSO. The purpose of this paper is to constrain the nature and the geometry
of the DSO. We compare 3D radiative transfer models of the DSO with the NIR
continuum data including polarimetry. In the analysis, we use basic dust
continuum radiative transfer theory implemented in the 3D Monte Carlo code
Hyperion. Moreover, we implement analytical results of the two-body problem
mechanics and the theory of non-thermal processes. We present a composite model
of the DSO -- a dust-enshrouded star that consists of a stellar source, dusty,
optically thick envelope, bipolar cavities, and a bow shock. This scheme can
match the NIR total as well as polarized properties of the observed spectral
energy distribution (SED). The SED may be also explained in theory by a young
pulsar wind nebula that typically exhibits a large linear polarization degree
due to magnetospheric synchrotron emission. The analysis of NIR polarimetry
data combined with the radiative transfer modelling shows that the DSO is a
peculiar source of compact nature in the S cluster $(r \lesssim 0.04\,{\rm
pc})$. It is most probably a young stellar object embedded in a non-spherical
dusty envelope, whose components include optically thick dusty envelope,
bipolar cavities, and a bow shock. Alternatively, the continuum emission could
be of a non-thermal origin due to the presence of a young neutron star and its
wind nebula.
