That's right. However but Chimps can experience human-like feelings and emotions although I don't know if they can feel empathy. Basically they can behave like a murderous psychopaths.
I know evolution isn't necessarily popular here, but I'll say it. There's only 5-7 million years between now and the common ancestor of chimps and humans. Of course they have many human-like traits. They do have complex emotions and high intelligence. Their DNA is almost identical to human DNA. However they're not human, they are animals.
Humanity was not around until humans began to communicate with God in a meaninful way, which was only several thousand years ago, not millions.
Chimpanzees must not be judged by human standards, it's not fair to the chimpanzees. They're not human, they don't have the capacity for human motivations and human vices. All of nature is pretty much "savage" and "bestial", from one protozooan absorbing another, to an animal dying of a parasitic infection, to a baby coming out severely malformed. I don't know why God allowed it to be that way, but that's how nature is. Singling out chimpanzees and maligning them is not fair or useful.
Only humans can sin.