That doesn't exclude him from being a psychopath at all.
Psychopath is a state of reduced empathy, not lack of. Doflamingo draws a clear borderline where empathy stops, and cares not for those out of the line. This line is true for anyone, but drawing such a tight nit zone and limiting empathy and remorse for all indicates psychopathy.Psychopath doesn't mean one can't love his mother. If one can only extend his/her empathy to his/her close kinsmen and no one else, then yes, it's a sociopath, and with ruthlessness mixed in, a clear sign of psychopath.
Well everything I've ever read about psychopathy said that means a complete lack of empathy and love. Some of them said that sociopaths may have some, if reduced capacity for that. But then again they were mostly net sources…
Either way real world psychology shouldn't be taked too seriously in fiction, just like with other sciences! Character's personalities and traits are just what they need to be to serve their role. We may try make diagnozes of their psyche, but they don't really mean anything unless the author meant the same thing. I doubt Oda wanted his villains explicitly to portray sociopathy. They just needed to be despicable bad guys for Luffy to take down.