I think you might have run into the exact thing I put in my comment: "not to be confused with ASPD", which is also sometimes called sociopathy. I use psychopathy and sociopathy differently (such that psychopathy is chosen while sociopathy is inherent) and choices like these can be an autistic trait. I'm not talking about empathic struggles, but rather a choice not to care too much about someone's emotions in a particular context. I don't know how to square these with the commonly accepted definitions because the commonly accepted definitions are kind of ridiculous (the terms psychopathy, sociopathy, and ASPD are collectively sort of ambiguous because they all each mean everything somehow; nearly everyone is confused about them in some way).

This is why I said psychopathy "can be" the selective inhibition of empathy, because by some definitions that's what it is. Other definitions like yours essentially define it as what I call sociopathy (simply being without empathy in the first place). I don't claim my definition to be the only definition because psychopathy can sort of mean either thing depending on who you ask, but I use my definition just for the sake of argument.