Someone who is strength training should have the flexibility to go on a weekly run and remove a day on the weights. That's heresy to some coaches who want to keep you in the gym.
This workout is based around compound movements to work as many muscles as possible in a short amount of time so you can easily fit them into your daily routine.
Simply put, as long as you are burning more calories than you consume, you should be able to lose weight. According to the researchers, there's a chance the theory won't hold water.