That is simply convection.
The wick does suck molten wax, and it goes up by capillary to the middle of the flame, but that movement is way to slow to explain the fast particles in your video. Moreover they are moving in the opposite direction!
Convection happens because the wick is hot, and it makes the wax around also hot, so the wax expands a little and gets lighter. Since hot wax is lighter it will go up (because of buoyancy). And since it goes up around the wick, it will go to the sides when it reaches the surface, then cools in contact with air and goes down.
Note how the red arrows curve to the sides when they reach the surface. That is what you see in the moving particles.
In your video you can even see the black particles moving towards the wick when they go down, doing full circles, just as in the graphic.
Usually, in convection the heat comes from below, as in this graphic from Wikipedia. The effect is similar, but instead of having the heat source at the bottom, it would be just in between two red arrows.