There are two phenomena that look cyclonic.

The larger ones have to do with motion on a sphere: Euler showed that any velocity vector on a sphere can be represented as a rotation about a point (called an Euler pole); tectonic plates move basically rigidly, so the whole things rotate around a point. When that point is very close to (or within) the plate, the rotation is quite visible. You can see this in the Antarctic plate, halfway between Antarctica and Madagascar.

The second is an artifact of the vector visualization that Beccario used. The atmosphere is a continuum, so particles move smoothly between one location and another (more or less). But tectonic plates have rigid boundaries, and dive under each other or slide rigidly past one another. But the visualization algorithm doesn't know about these boundaries, so it creates particle paths that cross the boundaries and appear to swirl around. This probably happens to some degree in the mantle below the plates, but not really at the surface, with minor exceptions that I won't get into now unless people really want to nerd out on microplate rotation.

I'm not sure about the data gap at the poles. That's probably a real gap in the dataset I used; I haven't looked into it.