Recently, much interest has emerged in fluid-like electric charge transport in various solid-state systems. The hydrodynamic behavior of the electronic fluid reveals itself as a decrease of the electrical resistance with increasing temperature (the Gurzhi effect) in narrow conducting channels, polynomial scaling of the resistance as a function of the channel width, substantial violation of the Wiedemann-Franz law supported by the emergence of the Poiseuille flow. Similarly to whirlpools in flowing water, the viscous electronic flow generates vortices, resulting in abnormal sign-changing electrical response driven by the backflow of electrical current. Experimentally, the presence of the hydrodynamic vortices was observed in low-temperature graphene as a negative voltage drop near the current-injecting contacts. However, the question of whether the long-ranged sign-changing electrical response can be produced by a mechanism other than hydrodynamics has not been addressed so far. Here we use polarization-sensitive laser microscopy to demonstrate the emergence of visually similar abnormal sign-alternating patterns in charge density in multilayer tungsten ditelluride at room temperature where this material does not exhibit true electronic hydrodynamics. We argue that this pseudo-hydrodynamic behavior appears due to a subtle interplay between the diffusive transport of electrons and holes. In particular, the sign-alternating charge accumulation in WTe2 is supported by the unexpected backflow of compressible neutral electron-hole current, which creates charge-neutral whirlpools in the bulk of this nearly compensated semimetal. We demonstrate that the exceptionally large spatial size of the charge domains is sustained by the long recombination time of electron-hole pairs.