I am not at all sure I am correct, but my best explanation is that in tracing the tortuous groove, the stylus is pulled along at a "speed" dependent upon the platter speed and the distance of the styus from the spindle. The ins and outs of the groove walls however cause rapid instantaneous changes in stylus velocity, in order for it to negotiate the groove. Each instantaneous change, because it forces a change in velocity at the stylus tip, is an "acceleration". Acceleration is defined as a change in velocity, up or down. So now you have a mass (the moving mass of the cartridge) that is constantly accelerating. This would create or rather require the stylus to endure tiny forces according to Newton’s First Law of Motion (F = ma). It is those tiny Newtonian forces, which have a vector direction in the general direction of the friction force, that add to the net skating force.
Then could you explain why if you put the stylus on a glass platter or blank vinyl disc, neither of which have a tortuous groove, the skating force still occurs ?