Love: an emotion of a strong affection and personal attachment. Love is also said to be a virtue representing all of human kindness, compassion, and affection —"the unselfish loyal and benevolent concern for the good of another".
Empathy: the experience of understanding another person's condition from their perspective. You place yourself in their shoes and feel what they are feeling.
There is no doubt that my uBPDexgf loved me. We shared tender moments. She so wanted to be known and loved.
I don't think BPD's love in the definition you shared with us. Actually, i'm sure of it. However they do want to be known and loved and hugged and be confirmed with the security they can get from you.
Someone with BPD does not understand the true meaning of love due to their malfunction in their head. They fill in the deep void within yourself which you perceive to be love, however we've all been living in that lie. Thats why it hurts so ing much to detach ourselves from that.