Hum, there are interesting things in that article, but it seems way too one-sided to me,

Think of it as a single message in a longer debate, spanning centuries. That's what an academic philosophers do, on their better days. ;) So, yes, this is not a "debate", this is a position piece, laying out arguments for only one side. Read that way, it's quite even-handed.

and it dwells upon confusion between two thesis which are very different : « empathy is not the only source of morality » (which I agree with) and « empathy is not a core part of morality » (which I disagree with).

Does it? On my reading, it's only arguing that "empathy is not the only source of morality," and then in section 5 "empathy should not be the only source of morality." I don't think it argues, anywhere, that empathy is not a /part/ of morality, or moral judgment.