Momentum transfer is the key idea. Flow is not apparent. Spherical field rotation is actually a decent way to conceive of electron motion: https://www.physics.mcmaster.ca/phys3mm3/notes/whatisspin.pd...
On first read, the mental model of atomic-scale gears meshing and turning at different rates (does direction matter? How do you think of amperage in terms of rotating shafts made of meshed gears?) more fraught with simplifying assumptions and unnecessary epicycle-style complications than the conventional hydrodynamic model.
Like the hydraulic analogy, this visualization is to help us understand not an exact movie of what's happening. Math may be better for that level of detail, for now. This visualization uses atoms, which is the main advantage over the hydraulic.