Yes, he did kill him. He knew Ra's was in the train, and he made a premeditated action, by telling Gordon to blow the tracks. Knowing that he had the equipment to get out himself, and knowing full well that the tracks would be blown, he himself caused the very fate for Ra's. Maybe if Gordon blew the tracks on his own accord, without being consulted by Batman, maybe I could see it that way, but seeing as it was all Batman's idea, I can't see it any other way. He lead him into a trap he knew he wouldn't be able to get out of.
Just because he says the 'magic' words of "I'm not going to kill you, but I don't have to save you", doesn't deny the fact that it was a premeditated trap for Ra's.
1. He didn't actually DO the actions that caused Ra's to die, though. Gordon did. This isn't a military hearing where its Batman's fault for giving Gordon an idea. This is real life, where people have to make moral choices despite the options other people provide them.
2. It wasn’t a trap for Ra’s. It wasn’t about killing Ra’s Al Ghul at all. It was about preventing the train from reaching Wayne Station to save Gotham City. Period.
If you really think Batman just flat out killed Ra's by telling Gordon to do something in case he failed to stop the train, then I don’t think you understand cause and effect. At least in context.
Because if you don’t physically act to kill someone yourself, then you aren’t the one who killed that person.
Now, if you set up a plan to kill that person, or a plan you set up results in that person’s death, did your actions indirectly lead to that person’s death? Possibly. Lots of things can indirectly lead to other things. You want to have that philosophical discussion, we can. But for you to honestly look at the scene in context and say “Batman directly killed Ra’s” is inaccurate.
You're still denying the fact that Batman clearly said he never meant to stop the train, and adding to the fact that he told Gordon to blow the tracks, it comes down to it being premeditated.
That’s not what Batman said at all. Look at the scene in context. He said “Who said anything about stopping it”? And why did Batman say that? What was the context of the words in the scene?
He said it in response to Ra’s saying “That’s why you can’t stop this train”. While Batman was getting choked to death.
When Batman says “Who said anything about stopping it”, he’s basically grasping at straws to survive, acknowledging that he knows the train can't be stopped and using that to surprise Ra's with his calm over that fact, simultaneously implying that he has an ace up his sleeve to throw Ra's further. He’s saying that because he’s trying to distract Ra’s, so Ra's will look up and see the towers collapsing and remove his attention from Bruce for that split second. Because otherwise, he’s going to die at Ra’s Al Ghul’s hands.
It’s a ploy to distract Ra's and gain the upper hand, not an admission or a statement of “My plan all along was to derail this train”. Before the event, he clearly says to Gordon "I may need your help". Derailing the train was a backup plan.