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I didn't see that in the video, but there are a couple of factors that would come into play...in that first video, the biggest problem I saw was that the alligator was still struggling when the snake had it swallowed to the rear legs. Odds are that he caused damage that led to the snakes death.
As far as the one in the original article - I would consider it an overly large meal...but probably not one that would kill the snake. (Barring any injuries sustained, the biggest concern would be whether the digestive system of the snake could deal with the croc's hide before decomposition gases caused the croc to swell)