Dynamic Stretches are great so long as you have obtained a deep core muscle temperature, prior to conducting them other wise you will be risking a strained / torn muscle
Best analogy - elastic band (when warm high elasticity) put in a freezer - low elasticity, and the band will be more prone to snapping if suddenly stretched too far. The same goes for your muscles. Ensure you warm up correctly in accordance to the physical activity you are to undertake.
I'd have thought that following this "dynamic stretching" routine would be more strenuous than the run you're supposedly warming up for! I need to know a routine to perform before my early morning jog/run. My pace is around 28mins for 5km. I seem to be able to run for 3-4 weeks before I start getting a twinge in a calf and have to lay off for a while. I know that a static stretch before a run is not a great idea, especially first thing in the morning.
This routine was to prepare for hockey matches and training - there are a lot of movements like the 'bunk beds' and sumo squats which are essential for the lower body profile of field hockey (you're constantly in a semi-squat position!) shorter versions are very doable, make sure you get a good range of motion to ensure you're stretching out as many muscle groups as possible - you can also do static stretches after your warm up (about 5-10 minutes into your run) but it all depends on how long you're out for really. I would say stretching out after a run would be more important than pre-run stretching (though obviously both should be done ideally) as your muscles are warmed up and so in the best state to get a good stretch!
@jaygoodman's rubber band analogy is so right - trying to stretch a cold muscle is just asking for trouble so always stretch after an initial cardio warm up which will prepare your muscles for a decent stretch!