Pre-workout cardio and stretching is often grossly underestimated in importance.
When warming up, a stretch position should not be held for longer than 10 – 15 seconds. When doing a preworkout stretch routine, a short hold is enough to loosen up stiff muscles, but it is not enough to loosen up a joint.
Stretches done with the intention of increasing range of motion (corrective stretching) should be done after a full length exercise routine, when muscles are fully warmed - or at periods of the day when you have a significant amount of time before your next bout of rigorous physical activity.
For warming up, you should never hold stretches for an elongated period of time as this can expand and loosen joints making them more susceptible to injury.
Though different studies have debated back and forth about the benefit of stretching cold muscles before jumping straight into a strenuous workout, gentle cardio and working the range of motion of joints is inarguably a good way to start any kind of exercise routine.
When you go from a standstill directly into some kind of high intensity cardio that raises your heart rate and engages your muscles without a warming up, it causes a greater amount of stress on your body. This is because when your heart tries to circulate your blood supply through constricted blood vessels to feed your muscle tissue, it meets resistance and causes your blood pressure to spike momentarily.
Aside from potential health repercussions, this can also interfere with your fitness progress by leading to premature fatiguing, because your body has to catch up to the demands of blood and oxygen flow that your muscles are requiring.
This short total body routine engages a multitude of muscle groups in a way that steadily increases blood flow and flexibility, rather than shocking your system with positions that tax the muscles before they are ready, or before you jump straight into a full blown cardio routine.
This would also serve as a great cool down workout. If you want to use this as a cool down, do the cardio component at the beginning of the workout, rather than at the end.