The massive evolved Wolf-Rayet stars sometimes occur in colliding-wind binary systems in which dust plumes are formed as a result of the collision of stellar winds. These structures are known to encode the parameters of the binary orbit and winds. Here, we report observations of a previously undiscovered Wolf-Rayet system, 2XMM J160050.7-514245, with a spectroscopically determined wind speed of $approx$3400 km s$^{-1}$. In the thermal infrared, the system is adorned with a prominent $approx$12$$ spiral dust plume, revealed by proper motion studies to be expanding at only $approx$570 km s$^{-1}$. As the dust and gas appear coeval, these observations are inconsistent with existing models of the dynamics of such colliding wind systems. We propose that this contradiction can be resolved if the system is capable of launching extremely anisotropic winds. Near-critical stellar rotation is known to drive such winds, suggesting this Wolf-Rayet system as a potential Galactic progenitor system for long-duration gamma-ray bursts.