  Evolution of massive stars is dominated by interactions within binary
systems. Therefore, it is necessary to investigate all forms of interaction in
binary systems that may affect the evolution of the components. One of such
laboratories is the massive eccentric binary system MACHO$\,$80.7443.1718
(ExtEV). We examine whether the light variability of the ExtEV can be explained
by a wind-wind collision (WWC) binary system model. We conducted an analysis of
broadband multi-color photometry of ExtEV, time-series space photometry from
TESS, ground-based Johnson $UBV$ photometry, and time-series spectroscopy. We
fitted an analytical model of light variations to the TESS light curve of
ExtEV. We rule out the possibility of the presence of a disk around the primary
component. We also argue that the non-linear wave-breaking scenario may not be
consistent with the observations of ExtEV. We refine the orbital parameters of
ExtEV and find evidence for the presence of a tertiary component. Using
evolutionary models we demonstrate that the primary component's mass is between
25 and 45$\,$M$_\odot$. We successfully reproduce light curve of ExtEV with our
model, showing that the dominant processes shaping its light curve are
atmospheric eclipse and light scattered in the WWC cone. We also estimate the
primary's mass-loss rate due to stellar wind for $4.5\cdot
10^{-5}\,$M$_\odot\,{\rm yr}^{-1}$. We conclude that ExtEV is not an extreme
eccentric ellipsoidal variable, but an exceptional WWC binary system. The mass
loss rate we derived exceeds theoretical predictions by up to two orders of
magnitude. This implies that the wind is likely enhanced by tidal interactions,
rotation, and possibly also tidally excited oscillations. ExtEV represents a
rare evolutionary phase of a binary system that may help to understand the role
of a companion-driven enhanced mass loss in the evolution of massive binary
systems.
