Not necessarily. It usually means somewhat selflessly feeling or understanding how they might feel enough to care about their wellbeing & treat them compassionately.

If you’re selective about the recipients of your empathy (eg, only those you care about or near you), then you’re not really an empath or a good one. Buddhists had empathy & compassion figured out. Jesus stated it, too, with love your enemies. I’ve frequently seen people try to wield empathy as a cudgel and miss the point.