The first video is fascinating. The second one does not really give a sense of what is happening.
I would think that for it to have truly linear (tangental) movement, the stylus must follow a straight line moving along the exact radius of the LP, theoretically ending at the spindle or center. It looks like this is accomplished by the base moving in and out and being hinged at two points and moving along an arch. But I don't see that the base moves the entire 5" or so that represent all of the grooves on the LP.
It's a very intriguing design and a difficult geometry problem to visualize. The bearings must be extremely silent and free of slop for there not to be any chatter considering all of the movement at the base where it can vibrate. Could Arnie or jfrech add some clarification?