Is it possible for a sociopath or a psychopath to genuinely love animals?

Not showing emotion is not the same as not having emotion.

The disorder is not really understood..but one of the indicators is practicing cruelty (physically inflicting pain or death) on animals.  It's almost like a milestone in their development.

I think the people you're referring to may have came to the conclusion that humans are not innocent (like animals) and thus undeserving of empathy.

It's not a view I share..and is perhaps something they will outgrow when they learn to see the beauty in humanity as well.

Psychopaths don’t like animals. They don't feel the guilt or regret for kicking, pinching, and hitting any animal in their way.

You don't seem to understand what Antisocial Personality Disorder is and what symptoms are need to actually make someone be labeled as either of those.  I am neither a psychopath or sociopath and I fit the description you put above. I could watch videos of 9/11 or hear about the next school shooting and not shed the slightest tear or bit of emotion. However, I will feel sad when I pass a dead coyote or deer along the local highway near me or hear about polar bears losing their home and end up entering villages in search of food. It is actually because I sincerely hate and spite humans. It's almost accurate to say I feel a sense of satisfaction when humans die.