Comment. Major Spoiler

You raise an interesting point. In the common law of most English-speaking countries, there is no general duty to come to the rescue of another. Many civil law systems, which are common in Continental Europe, Latin America and much of Africa, impose a far more extensive duty to rescue.

In the United States, as of 2009, ten states had laws on the books requiring that people at least notify law enforcement of and/or seek aid for strangers in peril under certain conditions: California, Florida, Hawaii, Massachusetts, Minnesota, Ohio, Rhode Island, Vermont, Washington, and Wisconsin. These laws are rarely applied in the United States, and are generally ignored by citizens and lawmakers (see The Myth of Moral Justice by Thane Rosenbaum). Anyway Gotham City is a proxy for New York City, which has no duty to rescue law, so I conclude that Batman had no legal duty to rescue Ra's Al Ghul.

Well he'd already gone out of his way to save his life once and look how he thanked him! Ra's wouldn't have stopped until Gotham was destroyed, so it was done to protect both himself and everyone in Gotham.
Plus I'm not sure Ra's couldn't have jumped from the train or something. Those last view seconds he just shut his eyes, like he knew he'd failed in his mission and wanted to go.
Anyway, it beats the usual action movie cliche in which the hero kills dozens of the main villain's henchmen to get to him, then refuses to kill the main villain.