They do a good job of making their case (with lots of studies to support their position) for strength training as your primary training modality and refuting the idea that you need to perform traditional aerobic exercise for health. In fact, they make the arguement against it. They make a great point about the benefits of a properly performed strength training program are.
"...if your resistance training is properly executed, and the result is the building of muscle, the ultimate gain to the human body is literally "everything". The metabolic subsystems that support an increased musculature increase their functional capacity along with the size of the muscles that employ them. The closer you get to realizing your muscular potential, the closer you get to optimizing your potential of your metabolic system or "support system."
I agree. Your muscles are the engines and your heart, lungs and blood vessels are simply the "supporting systems." Most people have the opposite idea. They view exercise as 'cardio' and neglect muscle strength and function.
I remember going to a conference and hearing the exercise physiologist from the University of Texas describe the physiological changes they measured in Lance Armstrong during the latter half of his career. Interestingly, his maximal oxygen uptake and heart function didn't change (they were already extremely high), but his average leg power output increased. This was most likely due to increased muscular efficiency, which has nothing to do with the heart, blood vessels, or lungs.
Building strength goes a long way. Proper, full-body strength training (not toning-that is a waste of time) should be central to everyone's exercise program.
And, even though strength training enhances "everything," I feel your training needs to include, mobility/stabiliy work, soft tissue work (foam rolling), planned active recovery, and probably additional metabolic conditioning (especially for greater fat loss or if your sport requires it). If you are an athlete, of course you will need to also practice your skills.