That walking form is completely wrong, and it's probably not a translation error either based on the images. In walking, jogging and sprinting, the left arm should go forward with the right leg and vice versa. Try to walk like the method she is describing, with the leg and arm on the same side going forward at the same time. It's simply not even possible to do. Did the author even try walking like that before writing this chapter?
https://en.wikipedia.org/wiki/Arm_swing_in_human_locomotion
"Swinging arms in an opposing direction with respect to the lower limb reduces the angular momentum of the body, balancing the rotational motion produced during walking. Although such pendulum-like motion of arms is not essential for walking, recent studies point that arm swing improves the stability and energy efficiency in human locomotion."