I don't think this Harvey ever really got to that point of obsession with randomness, duality, etc., either. It was much more just he wanted revenge on the guys who scarred him, with a bit of hating humanity for shunning him (or thinking they were shunning him) in thrown in.
It's not exactly the same, no, but that's the point. It's good to take the basics of the character and put them together in a fresh way. Two-Face has been portrayed in a lot of different ways over the past 82 years (yay, a multiple of two). This is just one more to add to the list. There is no single "correct" version.
As for the coin, it may seem like a gimmick, and often is, but handled correctly it is the heart of what makes Harvey insane as opposed to just malevolent: he is driven by a
mental-illness-produced irresistible impulse, which is manifested by the coin toss.
I am deeply uncomfortable with the tendency of Batman comics from the 1970s onward to assume his rogues are "insane." That perpetuates a false, damaging prejudice that stigmatizes mental illness. In fact, mentally ill people are far more likely to be victims of crime than perpetrators, largely because of the cultural prejudices perpetuated in fiction. Also, very few Batman villains actually meet the legal definition of insanity (a term that has no medical definition). They know the nature of reality and understand that their actions are criminal, so they are legally sane and competent to stand trial. Characterizing their personality disorders, neuroses, or compulsive behaviors as "insanity" just worsens the stereotype. So I welcome any Batman story that retreats from that deeply problematical and ableist trope.
In the Golden and Silver Ages, few of Batman's rogues were characterized as insane, just criminal. The closest thing to a mental illness was Catwoman turning out to be an amnesia victim and having essentially an alternate personality from her original Selina Kyle identity. The Riddler had a compulsive need to leave clues for Batman to solve, but that was OCD, not madness. There was even a 1950s story where the Joker
faked insanity to get access to a counterfeiter (I think) in an asylum and Batman & Robin foiled his scheme by proving him sane. As for Two-Face, his dependence on the coin could be seen as a fixation, but as originally portrayed, it was more of a conscious embrace of moral nihilism -- if random chance made him what he was, then he'd embrace random chance. It was a response to trauma, but no more so than Bruce Wayne responding to trauma by fixating on fighting crime.