I don't know how they do it precisely, but if I was to do it, I would sample a few points along the lines/curves to be drawn, add small random perturbations, and join them with smooth interpolating curves such as cubic splines. Apparently, all lines are drawn twice.
Possibly also, predefine Bezier curves to match a line segment or approximate an ellipse, transform them to align to the desired placement, then move the control points randomly.
In the example the characters are drawn the same way, because you don't have access to their definition as curves. You might also think to add small perturbations, writing character per character.