The Dark Knight very much feels like a Batman movie to me.
It has Batman in it fighting crime to the best of his abilities, even going so far as to cross major lines to get it done, alienating himself from his allies in the process at times (much like he has done in the comics).
It has James Gordon having to deal with the responsibilities of having to lead a police force, as both captain and commissioner, and fight crime to the best of his abilities alongside Batman, a relationship that both hurts and helps him, which is very much like the comics.
It has Harvey Dent using the law to fight crime, both helping Batman and Gordon and using their help in order to succeed, but his own personal flaws cause him to become a criminal when tragedy brings his true nature to the forefront. As a result, he goes from one of Batman’s allies to one of Batman’s enemies. This is very much like the comics.
It has The Joker, causing absolute chaos and anarchy all for the purpose of having fun, as well as exposing what he perceives as hypocrisy from the so-called "normal people" by doing horrible things to them that pushes them to the breaking point, all the while inspiring fear among Gotham citizens and making himself enemy #1 in Gotham. This is very much like the comics.
And just to be clear, I do like Batman Begins and think it has the right atmosphere. There's just something cold and clinical about TDK compared to it.
Some of Batman's allies get hurt and or killed in his battle with The Joker, much like has happened in the comics.
Batman fights gangsters and mobsters, much like he has done in the comics. He uses his skills and gadgets to pull off spectacular feats of heroism, much like does in the comics all the time. He works with and fights the Gotham police force, much like he does in the comics.
The Joker kills people without mercy, without remorse, and takes pleasure and great fun in doing it, like he has done in the comics since the 70's and when he was first created.
Alfred is there to comfort him, and give him tough love and advice, like he always is doing in the comics.
Bruce Wayne's public persona in Gotham is that of a good looking rich playboy who is incompetent and irresponsible, because Bruce creates that persona so no one could tie Bruce Wayne and Batman together, which is the way it's been in the comics for years.
So in what way is The Dark Knight NOT a Batman movie again? I am confused.