I dunno... I'm just not 'feeling' it.
Seriously, I think "empathy" is on a spectrum, much like intellectual intelligence. Some people are better tuned to the emotional state of others around them. Some, like me, have to work hard at it. If I run over someone's feelings, it's very likely that I'm completely unaware of having done so (except with some BDF-type people... then it's probably intentional).
The Bible doesn't list all the giftings that humans possess. Just think of all the ways in which people can be gifted (or ungifted) differently within the realm of language: translation, learning other languages, grammar, spelling, rhetoric, persuasion, journalism, poetry, fiction, and humour.
I'm sure "empathy" is a gifting just like so many others. The fact that other religions and philosophies have identified and developed it further doesn't necessarily mean it isn't of God originally. Rather, it means that we need to be cautious and use the wisdom and discernment available to us as believers.