Warmup and stretching are orthogonal to each other. Warmup is important, stretches pre-exercise are not and may be harmful in terms of injury risk for that workout. Doing dynamic stretches overall is good improving your flexibility, though. Overall you might very well have done yourself more good than harm, but you'd likely do yourself even more good by warming up a different way and doing your dynamic stretches at a different time.

"Getting your muscles moving" does not require a stretch, you can keep your movements well away from pushing your range of motion.