Where is he a psychopath in this?
Caesar is not a psychopath, in the clinical sense. He is a lot of things : a dictator, ruthless, without mercy, sadistic, megalomaniac. Evil, given our moral compass, sure. Surrounded by true psychopaths like Vulpes, absolutely. But Caesar himself is not a psychopath, even quite the contrary. If he was a psychopath, then, all our ancestors from Antiquity were also psychopaths, and we know it's not the case.
A psychopath doesn't have the ability to project himself into other people's emotions, to conceptualize them and to take them into consideration. Caesar, on the other hand, has built his entire faction with the feelings of the people around him. Every single action he made was meant to create an emotion in an audience : terror, respect, adoration, justice etc. He may not show
pity, he may not
care if he hurts the feelings, but his entire strategy is based on them. He understands the narrative that leads them.
In fact, if he suddenly stopped being ruthless, he could very well be attacked by his own men. Lanius and Vulpes wouldn't understand if Caesar suddenly showed mercy, and started to obey a social contract. They'd kill him. Caesar knows that his myth, fueled by brutality, is what keeps him alive. Boy is probably terrified by his own men (like Stalin or Blackbeard), and has to keep going deeper and deeper into brutality to keep the myth alive (who knows if Caesar didn't cry for Joshua, for example ? Nobody but himself). Without the myth, there is no legion. Without legion, there is no conquest. And in his mind, without conquest, humanity is doomed to be enslaved by inferior minds, exposed to danger, tribalism, injustice and the repetition of the errors of the past. Without the myth, the Legion will spit in civil war between Vulpes, Lanius and the other generals (Caesar knows his history). In Caesar's mind, preventing that is worth all the brutality.
Remove the social (the law) and spiritual (religion) contract that say that life is sacred, and you would have trouble explaining to someone why it's bad to kill 10 people, if it's to save an important life, or a hundred lives. The thing is, Caesar removed these abstract elements which are the only ones backing the sanctity of human life, by deifying himself. Because his entire character is built on the idea of someone who never feared higher powers (neither the NCR, nor God, nor the followers of the apocalypse, nor the tribe that held him hostage with Calhoun and Joshua). Ignoring higher powers doesn't makes a man a psychopath. A cold and ruthless killer, absolutely. Joshua even shows an interesting contrast, as a true psychopath who struggles with his spiritual contract that keeps him from going full berzerk.
Vipers are in the same situation. But are they all psychopaths ? Of course not. They are probably normal people, but given their context, they believe that they are doing the good work for their souls (spiritual contract) and their masters, the daughters of Hecate (social contract) and that you stand in their way. They are the products of an environment with a new spiritual and social contract, just like Caesar. The exact same guy in another environment would be a nice guy.
A psychopath suppresses the impulses of anxiety, anger and brutality when things aren't in control. Caesar does the exact contrary. He shows stress and anxiety when speaking about his tumor. He expresses regret when speaking about his mother. He gets furious if things aren't in control and can strike hard to retaliate.
A psychopath is the result of genetics, when Caesar's behaviour is clearly a result of his environment : father killed by raiders, too intelligent for his surroundings as a scholar, held hostage by brutal tribes who only understand the law of the strongest etc.