I don't think he knew, he says that here because he is not the real Joker, he is an hallucination he is having and is basically incarnating all of Batman's fears and insecurities.
The scene in this video is part of the story, and takes place after Batman finds out that Jason is still alive, so it makes sense that the imaginary 'Joker' would taunt Batman, since the imaginary Joker exists in Batman's mind, and so has full access to Batman's memories, and so is aware of Jason being alive and having been brainwashed into hating Batman. What doesn't make sense is that when Jason reveals who he is to Batman, and Batman is amazed to find out that Jason has been alive all of this time, the imaginary Joker immediately confesses to having faked Jason's murder. The imaginary Joker, exists merely as a figment of Batman's imagination, wouldn't know what the real Joker had done, and would instead believe that Jason was dead, simply because Batman believes it. And given that up to Jason's revealing his true identity, Batman has been hallucinating things, then logically it would be much more likely that Jason is in fact dead, and that Batman is imagining Jason being alive and standing in front of him (Batman). But Batman never considers this, instead he immediately accepts that Jason is alive and talking to him. I mean, Batman is right, of course, but logically the chances of Batman being wrong are massively larger than him being right.
That was a hallucination. Batman actually did break his neck and the conversation that follows is all in his head. That's why even after he sets the corpse on fire he still tells it to stop laughing, because from his perspective it never stopped.
The Joker is only a figment of Batman’s imagination in Arkham Knight since he died in Arkham City (not by Batman’s hand) So technically Batman didn’t kill him
The first time I watched the video i thought the text said “Kill Jerker” the second time I watched this video I thought it said “Kill Jonkler”… I think Arkham Subreddit brainrot got into me
Wait wait waittttttt!!!!! Hold up, isn't Batman first rule is that he's not supposed to kill anyone regardless whether they're a criminal or not, what cause him to now kill????
because it was a hallucination brought on by Scarecrow's fear toxin and the joker's blood in Batman's veins, the whole game also centres on the influence of Joker and the clown prince's persistence to turn Batman into Joker, all it takes is one bad day right ?