Odly enough, your "pivot kicking" in the first video and "step n kicking" in the second. Watch closely, your taking a step out in the second video. You have really good hip flexibility brotha.
What your doing in the second video is "shortening the arc" by using that step. Neither is "wrong" per se and I like the angle your shin is traveling. What is wrong, IMO is using that step if your going to be pivot kicking. It basically defeats the entire principal/purpose and avantage of that style of kicking. If your gonna step, step n open your hips and you'd be better off just swinging it through, or you end up with a more telegraphed kick that robs itself of power. Your taking the step, but not opening the hips with that step, which is the entire purpose of using that step in the first place. This is the reason your kick looks telegraphed is because your stepping to open the hips (but leaving them closed) then using the upper body mechanics as if you weren't taking that step....... as other posters noted, your leading too early with that shoulder because your not opening the hips when your stepping (if your gonna step n kick, see below in red where explained in prior post).
So here's what ya wanna try (low kicking) if your really focusing on pivot kicking for your low kicks. Just like you did in the initial video, you were pivot kicking. But in trying to shorten the arc of the kick you compensated in the second video by using a step. Instead of using that step, getting your weight farther forward (as described in prior post) over your hips and delaying that pivot will sink your weight heavier on to that lead leg. In which case you'll be able to use that same arc you did when swinging 360degrees, but you'll only have to swing 180degrees like you did in second clip. The ball of that foot on kicking leg should really drive down into the floor like your trying to "hammer a nail straight into the floor". This requires great balance, particularly when shadowkicking, but you appear to have the hip flexibility to do it. When you get it right, you'll be able to throw your high and mid kicks with the same downward chopping motion and not have to spin the full 360degrees....... (Feitosa). This style of kicking really requires the pivot foot to be far more drastically torqued (counterclockwise) than a typical MT kick. See pic below, give ya an idea. This was for a high kick, but you can see where the point of the hip n shoulder on kicking leg side are well ahead (pointing downward) of the heel on the pivot foot (also why my knees are completely shredded from years of doing this).
If your going to practice this method of kicking, work on shadowkicking with the 360 degree spin for mid/high kicks, only imagine kicking a football off a tee on your follow through the exact opposite direction of the target your kicking at (pic above, imagine if I were to turn my head, arch back and pull up chin. looking straight the opposite direction, kicking the football off tee). Once you get that mechanically, all you have to do to shorten the arc on the kick/follow through is sink down heavier on the post leg. So instead of the kick swing back through (kicking football off tee) it just drives straight down into the mat (hammer hitting nail through mat analogy).