Rorschach cries in the comic/novel at the end, not at his own death, his is something as you say he does not care about as he puts in his journal. He is crying for several reasons i believe, for starters his friends have abandoned him, his beliefs in moral justice and in a way they have given up on the world and given in to a terrorist. Lastly he's appalled that the state of the world has come down to this.
Despite his cold hard, insane exterior Rorschach cares about the world and the good people in it, there is only good and evil no grey areas.