If you notice in the first video the bowler is side on from lower part of the body and front on from the upper part of the body. I will never encourage that as it's not alligned. At the point of release his body is falling and in an awkward position. You either are front on, semi or side on from both lower and upper part.
In the second video we have tried to make him more side on from up as it's easier to change the upper portion than the lower portion of the body. He is watching the batsmen from inside of his non bowling arm, also a small pause at the point of backfoot landing for better use of the body in the delivery. By this his allignment is better, he's watching his target from a better position at the release of delivery and his back foot is also finishing better hence he will be more accurate in the longer run.