The routine will make next to no difference to fat loss, fat loss is largely due to diet.
Similar but not the same:
Atkins counts the carbs in vegetables, CT doesn't.
CT has a carb up periodically, Atkins doesn't.
Atkins has several phases, most people think of the Atkins diet being the Atkins diet induction phase.
BTW; not sure which article you are reading but CT has revised his initial article with the "Refined Physique Transformation" article.