The empathy part is rather interesting, but killing another player doesn't necessarily imply a lack of empathy. While there are players out there, across every game, who take pleasure in trolling and causing grief to others, they are actually a minority. Most players engage in PvP because they enjoy engaging in PvP. While you could argue that they could always go for consensual PvP, you do get a certain rush from a 'hunt' and a fight which isn't staged.
Agreed, killing another player doesn't imply a lack of empathy, but I'd argue the idea that a loss in game isn't something ever worth caring about is. A lack of empathy doesn't need to be as malicious as actively trying to elicit negative reactions and I'd argue typically isn't.