Where the speed swing comes from
As the cross rotates, it rocks back and forth in a plane that is tilted relative to the output shaft. The output angle follows tan(output) = tan(input) / cos(beta), so the output alternately gains and loses on the input.
Over a whole turn the average speed is exactly the input speed, but the instant speed swings between input x cos(beta) and input / cos(beta). The scene uses that exact relationship, with the shafts slowed so you can see it.
Fixing it with two joints
Vehicle drive shafts use two universal joints with equal angles and their inner yokes lined up. The second joint undoes the first joint's speed swing, so the axle turns smoothly. Constant velocity joints solve the same problem with balls in grooves.