Yes, but that has nothing to do with what we were discussing. So the difference between a psychopath and another person in the dna level are the same as the difference between an able-bodied and a person with congenital disability. And we are all in this species which have 99.9% similarity. So either we can empathize with a psychopath or we cannot empathize with anyone who has a significant difference from us, unless you argue the dna level difference between a psychopath and a non-psychopath is somehow more pronounced than other variety of characteristics

Then do we really have empathy, when we cannot empathize with anyone but those who are exactly like us?

It seems to me that the presumption behind your logic is that we cannot put ourselves in the shoes of someone who is fundamentally different from us, just like it was investigated in the article "what is it like to be a bat". However, we should clarify what we mean by "fundamentally". For example, can an extrovert empathize with an introvert? Can an able person empathize with with someone with disability? Can a heterogeneous empathize with a queer?
In my view, all these cases depend on our perspective-taking abilities plus our compassionate disposition. The same goes for empathizing with a psychopath

Taking into consideration how evolution works, might help with difficult questions like this one. Only those characteristics that lower a person's chance of reproduction or the chances of survival before reproduction, get eliminated by natural-selection processes. Hence, not all bad habits are left out by evolution. For example, although unpleasant, nail biting doesn't restrict a person's chance of reproduction or survival up to the age that they can reproduce. Smoking and bing eating or drinking are in the same category; although really harmful, they do not affect reproduction chances hugely.