  Context. The structure of the wind from the cool giants in symbiotic binaries
carries important information for understanding the wind mass transfer to their
white dwarf companions and its fuelling. Aims. In this paper, we indicate a
non-spherical distribution of the neutral wind zone around the red giant (RG)
in the symbiotic binary star, EG And. Methods. We achieved this aim by
analysing the periodic orbital variations of fluxes and radial velocities of
individual components of the H$\alpha$ and [OIII]$\lambda$5007 lines observed
on our high-cadence medium (R $\sim$ 11 000) and high-resolution (R $\sim$ 38
000) spectra. Results. The asymmetric shaping of the neutral wind zone at the
near-orbital-plane region is indicated by: (i) the asymmetric course of the
H$\alpha$ core emission fluxes along the orbit; (ii) the presence of their
secondary maximum around the orbital phase $\varphi = 0.1$, which is possibly
caused by the refraction effect; and (iii) the properties of the H$\alpha$
broad wing emission originating by Raman scattering on H$^0$ atoms. The wind is
substantially compressed from polar directions to the orbital plane as
constrained by the location of the [OIII]$\lambda$5007 line emission zones in
the vicinity of the RG at/around its poles. The corresponding mass-loss rate
from the polar regions of $\lesssim 10 ^{-8}$ Msun/yr is a factor of $\gtrsim
10$ lower than the average rate of $\approx 10^{-7}$Msun/yr derived from
nebular emission of the ionised wind from the RG. Furthermore, it is two orders
of magnitude lower than that measured in the near-orbital-plane region from
Rayleigh scattering. Conclusions. The startling properties of the nebular
[OIII]$\lambda$5007 line in EG And provides an independent indication of the
wind focusing towards the orbital plane.
